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\title{Set Theoretic Rajan Transform and its Properties}
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\begin{document}

             \author[1]{G.  Prashanthi}

             \author[2]{G.  Sathya}

             \author[3]{Manish  Prateek}

             \author[4]{E. G.  Rajan}

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\date{\small \em Received: 7 December 2019 Accepted: 31 December 2019 Published: 15 January 2020}

\maketitle


\begin{abstract}
        


In this paper, we describe the formulation of a novel transform called Set Theoretic Rajan Transform (STRT) which is an extension of Rajan Transform (RT). RT is a coding morphism by which a number sequence (integer, rational, real, or complex) of length equal to any power of two is transformed into a highly correlated number sequence of same length. STRT was introduced by G. Sathya. In STRT, RT is applied to a sequence of sets instead of sequences of numbers. Here the union (U) is analogous to addition (+) operation and symmetric difference (~) is analogous to subtraction (-). This transform satisfies some interesting set theoretic properties like Cyclic Shift Invariance, Dyadic Shift invariance, Graphical Inverse Invariance. This paper explains in detail about STRT and all of its set theoretic properties. 

\end{abstract}


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\section[{Introduction}]{Introduction}\par
n STRT, given a sequence of sets X(n) of length N, which is a power of two, first it is divided into the first half and the second half each consisting of (N/2) points so that the following holds good : G(j)=X(i)UX(i+(N/2)); 0?j?(N/2); 0?i?(N/2) H(j)=X(i)\textasciitilde X(i-(N/2)); 0?j?(N/2); 0?i?(N/2) Now each (N/2) -point segment is further divided into two half's each consisting of (N/4) points so that the following holds good: G1(k)=G(j)UG(j+(N/4)); 0?k?(N/4); 0?j?(N/4) G2(k)=G(j)\textasciitilde G(j-(N/4)); 0?k?(N/4); 0?j?(N/4) H1(k)=H(j)UH(j+(N/4)); 0?k?(N/4); 0?j?(N/4) H2(k)=H(j)\textasciitilde H(j-(N/4)); 0?k?(N/4); 0?j?(N/4) This process is continued till no more division is possible. The total number of stages thus turns out to be log2N. Then the signal flow graph for STRT of length eight would be of the form shown in the Fig.  {\ref 1}. 
\section[{Fig. 1: Signal Flow graph of STRT}]{Fig. 1: Signal Flow graph of STRT}\par
Unlike RT, duality doesn't hold good in STRT. If X(n) is a set sequence of length N=2k, k>0 then its Set Theoretic Rajan Transform is denoted by Y(k). Consider a set sequence X(1)=\{1,2\}, X(2)=\{3,4,6\}, X(3)=\{4,5\}, X(4)=\{1,5\}, X(5)=\{1,4,5\}, X(6)=\{3,4,5\}, X(7)=\{2,6\}, X(8)=\{1,4,6\}. Then STRT is computed as follows. 
\section[{Input set sequence}]{Input set sequence}\par
Stage \#1 Stage \#2 
\section[{c) Dyadic Shift Invariance property}]{c) Dyadic Shift Invariance property}\par
The term 'dyad' refers to a group of two, and the term 'dyadic shift' to the operation of transposition of two blocks of elements in a sequence. For instance, let us take X(n)=\{1,2\},\{3,4,6\},\{4,5\}\{1,5\},\{1,4,5\}, \{3,4,5\}, \{2,6\},\{1,4,6\} and transpose its first half with the second half. The resulting sequence Td(2)[Xn)]=\{1,4,5\}, \{3,4,5\},\{2,6\}. \{1,4,6\},\{1,2\},\{3,4,6\},\{4,5\},\{1,5\} is the 2-block dyadic shifted version of X (n). The symbol Td(2) denotes the 2-block dyadic shift operator. In the same manner, we obtain Td(4)[Td(2)[X(n)]]=\{2,6\},\{1,4,6\} \{1,4,5\},\{3,4,5\},\{4,5\},\{1,5\},\{1,2\},  {\ref \{3,} {\ref 4,} {\ref 6\} and Td(8)}  {\ref [Td (4)}[Td(2)[X(n)]]]=\{1,4,6\},\{2,6\},\{3,4,5\}, \{1,4,5\},\{1,5\}, \{4,5\},\{3,4,6\},\{1,2\}. One can easily verify that all these dyadic shifted sequences have the same Y(k), that is, \{1,2,3,4,5,6\},\{2,3\},\{1,3,6\},\{3,6\}, \{2,4,5,6\},\{2\},\{4,6\}, \{4,6\}. There is yet another way of dyadic shifting input sequence X(n) to Td(2)  {\ref [Td(4)}  {\ref [Td(8)}[X(n)]]]. Let us take X(n) =,\{1,2\}, \{3,4,6\},\{4,5\}\{1,5\},\{1,4,5\},\{3,4,5\},\{2,6\}, \{1,4,6\} and obtain following dyadic shifts: Td(8)[X(n)]= \{3,4,6\},\{1,2\},\{1,5\},\{4,5\},\{3,4,5\},\{1,4,5\}, \{1,4,6\},\{2,6\} Td(4)  {\ref [Td(8)}[X(n)]]=\{1,5\},\{4,5\},\{3,4,6\}, \{1,2\},\{1,4,6\}, \{2,6\},  {\ref \{3,} {\ref 4,} {\ref 5\},}\hyperref[b2]{\{1,} {\ref 4,} {\ref 5\} and Td(2)}  {\ref [Td(4)}   {\ref [Td(8)[X(n)}]]]= \{1,4,6\},\{2,6\},\{3,4,5\},\{1,4,5\},\{1,5\}, \{4,5\},\{3,4,6\}, \{1,2\}. Note thatTd(2)  {\ref [Td(4)}  {\ref [Td(8) [X(n)}]]]= Td(8)  {\ref [Td(4)} [Td(2)[X(n)]]]. One can easily verify from the above that other than Td(4)[Td(2)[X(n)]] and Td(8)[X(n)], all other dyadically permuted sequences fall under the category of the cyclic permutation class of X(n) and  {\ref X-1(n)}. This amounts to saying that the cyclic permutation class of X(n) has eight non-repeating independent sequences, that of X-1(n) has eight non-repeating independent sequences and the dyadic permutation classes of X(n) has two non-repeating independent sequences. To conclude, all these 18 sequences could be seen to have the same Y(k).Set Theoretic Rajan Transform has many emerging applications. It can be used as a powerful tool in encrypting digital (color) images. It has many other applications in domains like Signal Processing and Higher Order Mathematics. 
\section[{III. Application of strt in the Study of}]{III. Application of strt in the Study of}\par
Extended Topological Filters Defined Over a Finite Set\par
Consider a finite set X=\{a,b,c\}. Then its power set is  {\ref \{\{?\},\{a\},\{b\},\{c\},\{a,b\},\{a,c\},\{b,c\},\{a,b,c\}\}.} One can construct a filter set F whose elements satisfy the following property: 'Any element of F ensures the presence of all its super sets present in the power set of X. For example consider a set X = \{a,b,c\}. The power set is  {\ref \{?, \{a\}, \{b\}, \{c\}, \{a,b\}, \{a,c\}, \{b,c\}, \{a,b,c\}\}.} The set F = \{\{a\}, \{a,b\}, \{a,c\}, \{a,b,c\}\} is a valid topological filter set since every element in F ensures the presence of all its super sets. One can construct 18 such topological filters from the ground set X as shown in table  {\ref 1}.\par
Table  {\ref 1}: List of topological filters from X = \{a,b,c\} 
\section[{Filters}]{Filters}\par
Filter Contents Cardi nality  {\ref \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\},\{b,c\},\{a,b,c\} \} 7 F2 \{\{a\},\{b\},\{a,b\},\{a,c\},\{b,c\},\{a,b,c\}\} 6 F3 \{\{a\},\{c\},\{a,b\},\{a,c\},\{b,c\},\{a,b,c\}\} 6 F4 \{\{b\},\{c\},\{a,b\},\{a,c\},\{b,c\},\{a,b,c\}\} 6 F5 \{\{a\},\{a,b\},\{a,c\},\{b,c\},\{a,b,c\}) 5 F6 \{\{b\},\{a,b\},\{a,c\},\{b,c\},\{a,b,c\}) 5 F7 \{\{c\},\{a,b\},\{a,c\},\{b,c\},\{a,b,c\}) 5 F8 \{\{a\},\{a,b\},\{a,c\},\{a,b,c\}\} 4 F9 \{\{b\},\{a,b\},\{b,c\},\{a,b,c\}\} 4 F10 \{\{c\},\{a,c\},\{b,c\},\{a,b,c\}\} 4 F11 \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c\}\} 4 F12 \{\{a,b\},\{a,c\},\{a,b,c\}\} 3 F13 \{\{a,b\},\{b,c\},\{a,b,c\}\} 3 F14 \{\{a,c\},\{b,c\},\{a,b,c\}\} 3 F15 \{\{a,b\},\{a,b,c\}\} 2 F16 \{\{a,c\},\{a,b,c\}\} 2 F17 \{\{b,c\},\{a,b,c\}\} 2 F18} \{\{a,b,c\}\} 1 
\section[{F1}]{F1} 
\section[{Lattice of topological filters}]{Lattice of topological filters}\par
The lattice <?, ?> is constructed as given in Fig. \hyperref[fig_0]{2} whose elements are 18 topological filters defined over the ground set X = \{a,b,c\}. Note that the symbol ? denotes the partial order relation of 'subset of'. To apply STRT to a filter chain, the length of the chain should be a power of 2. The length of the chain in this case is 7. So the null set \{ \} is considered as the eighth filter as it is a subset of any set. By applying STRT to these 48 filter chains, we get their corresponding spectra. Table \hyperref[tab_0]{2} gives the STRT spectra of all 48 linear filter chains.   {\ref F1 \{\{a\},} {\ref \{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref \} ,} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} F18 \{\{a,} {\ref b,} {\ref c\}\} \{\{a\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\}\} \{\{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\}\} \{\{a\},} {\ref \{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\} \} \{\{a\},} {\ref \{b\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{a\},} {\ref \{c\},} {\ref \{a,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} Filter chain \# 4 and its STRT spectrum F1 \{\{a\},} {\ref \{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{a\},} {\ref \{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{a\},} {\ref \{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{a\},} {\ref \{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} F2 \{\{a\},} {\ref \{b\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{a\},} {\ref \{b\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{a\},} {\ref \{b\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{c\}\} F5 \{\{a\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\} ,} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{a\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\} ,} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{b\},} {\ref \{c\}\} \{\{a\},} {\ref \{b\},} {\ref \{c\}\} F11 \{\{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{a\},} {\ref \{b\}\} \{\{a\},} {\ref \{c\}\} F12 \{\{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{a\},} {\ref \{b\},} {\ref \{c\},} {\ref \{b,} {\ref c\}\} \{\{a\},} {\ref \{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\}\} \{\{a\},} {\ref \{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} F16 \{\{a,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{a\},} {\ref \{b\},} {\ref \{a,} {\ref b\},} {\ref \{b,} {\ref c\}\} \{\{a\},} {\ref \{b\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{c\},} {\ref \{a,} {\ref b,} {\ref c\}\} F18 \{\{a,} {\ref b,} {\ref c\}\} \{\{a\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\} \} \{\{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\}\} \{\{a\},} {\ref \{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{a\},} {\ref \{b\},} {\ref \{a,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{a\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref b,} {\ref c\}\} F5 \{\{a\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c \},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{a\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{b\},} {\ref \{c\}\} \{\{a\},} {\ref \{b\},} {\ref \{c\}\} F11 \{\{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a ,} {\ref b,} {\ref c\}\} \{\{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c \}\} \{\{a\},} {\ref \{b\}\} \{\{a\},} {\ref \{c\}\} F13 \{\{a,} {\ref b\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{a\},} {\ref \{b\},} {\ref \{c\},} {\ref \{a,} {\ref c\}\} \{\{a\},} {\ref \{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c \},} {\ref \{b,} {\ref c\}\} \{\{a\},} {\ref \{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} F17 \{\{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{a\},} {\ref \{b\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\}\} \{\{a\},} {\ref \{b\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b ,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{c\},} {\ref \{a,} {\ref b,} {\ref c\}\} F18 \{\{a,} {\ref b,} {\ref c\}\} \{\{a\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\}\} \{\{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{b,} {\ref c\}\} \{\{a\},} {\ref \{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c \}\} \{\{a\},} {\ref \{b\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{a\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref b,} {\ref c\}\}} Filter chain \# 7 and its STRT spectrum  {\ref \{\{a\},\{b\},\{c\},\{a,b \},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c \}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} F2 \{\{a\},\{b\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{c\}\} F5 \{\{a\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{a\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{b\},\{c\}\} \{\{a\},\{b\},\{c\}\} F11 \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c \}\} \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c \}\} \{\{a\},\{b\}\} \{\{a\},\{c\}\} F14 \{\{a,c\},\{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c \},\{b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} F16 \{\{a,c\},\{a,b,c\}\} \{\{a\},\{b\},\{a,b\},\{b,c\}\} \{\{a\},\{b\},\{a,b\},\{a,c\},\{b, c\}, \{a,b,c\}\} \{\{c\},\{a,b,c\}\} F18 \{\{a,b,c\}\} \{\{a\},\{a,b\},\{a,c\},\{b,c\}\} \{\{b\},\{c\},\{a,c\},\{b,c\}\} \{\{a\},\{b\},\{c\},\{a,c\},\{b,c\}, \{a,b,c\}\} -\{?\} \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c \}\} \{\{a\},\{b\},\{a,c\},\{a,b,c\}\} \{\{a\},\{c\},\{b,c\},\{a,b,c\}\}} Global Journal of Computer Science and Technology 
\section[{F1}]{F1}\par
Volume XX Issue I Version I 59 Year 2020 
\section[{( ) D}]{( ) D}\par
Filter chain \# 8 and its STRT spectrum Filter chain \# 9 and its STRT spectrum Filter chain \# 10 and its STRT spectrum  {\ref \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a ,c\}, \{b,c\},\{a,b,c\}\} F2 \{\{a\},\{b\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{c\}\} F5 \{\{a\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{b\},\{c\}\} \{\{a\},\{b\},\{c\}\} F1 1 \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c \}\} \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c \}\} \{\{a\},\{b\}\} \{\{a\},\{c\}\} F1 4 \{\{a,c\},\{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\},\{b,c \}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a ,c\}, \{b,c\},\{a,b,c\}\} F1 7 \{\{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{a,b\},\{a,c\}\} \{\{a\},\{b\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{c\},\{a,b,c\}\} F1 8 \{\{a,b,c\}\} \{\{a\},\{a,b\},\{a,c\},\{b,c\}\} \{\{b\},\{c\},\{a,c\},\{b,c\}\} \{\{a\},\{b\},\{c\},\{a,c\},\{b ,c\}, \{a,b,c\}\} -\{?\} \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c \}\} \{\{a\},\{b\},\{b,c\},\{a,b,c\}\} \{\{a\},\{c\},\{a,c\},\{a,b,c \}\} F1 \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a ,c\}, \{b,c\},\{a,b,c\}\} F2 \{\{a\},\{b\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{c\}\} F6 \{\{b\},\{a,b\},\{a,c\},\{b,c\},\{a, b,c\}\} \{\{b\},\{a,b\},\{a,c\},\{b,c\},\{a, b,c\}\} \{\{a\},\{c\}\} \{\{a\},\{b\},\{c\}\} F11 \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c\} \} \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c\} \} \{\{a\},\{b\}\} \{\{b\},\{c\}\} F12 \{\{a,b\},\{a,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\},\{b ,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a ,c\}, \{b,c\},\{a,b,c\}\} F15 \{\{a,b\},\{a,b,c\}\} \{\{a\},\{b\},\{a,c\},\{b,c\}\} \{\{a\},\{b\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{c\},\{a,b,c\}\} F18 \{\{a,b,c\}\} \{\{b\},\{a,b\},\{a,c\},\{b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\}\} \{\{a\},\{b\},\{c\},\{a,b\}, \{a,c\},\{a,b,c\}\} \{?\} \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c\} \} \{\{a\},\{b\},\{a,b\},\{a,b,c\}\} \{\{b\},\{c\},\{a,c\},\{a,b,c \}\} F1 \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\} ,\{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c \},\{b,c\},\{a,b,c\}\} F2 \{\{a\},\{b\},\{a,b\},\{a,c\},\{b,c\} , \{a,b,c\}\} \{\{a\},\{b\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{c\}\} F6 \{\{b\},\{a,b\},\{a,c\},\{b,c\},\{a, b,c\}\} \{\{b\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{a\},\{c\}\} \{\{a\},\{b\},\{c\}\} F11 \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c\} \} \{\{a,b\},\{a,c\},\{b,c\},\{a,b, c\}\} \{\{a\},\{b\}\} \{\{b\},\{c\}\} F12 \{\{a,b\},\{a,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\},\{b,c \}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c \}, \{b,c\},\{a,b,c\}\} F16 \{\{a,c\},\{a,b,c\}\} \{\{a\},\{b\},\{a,b\},\{b,c\}\} \{\{a\},\{b\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{c\},\{a,b,c\}\} F18 \{\{a,b,c\}\} \{\{b\},\{a,b\},\{a,c\},\{b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c \},\{a,b,c\}\} -\{?\} \{\{a,b\},\{a,c\},\{b,c\},\{a,b, c\}\} \{\{a\},\{b\},\{a,c\},\{a,b,c\}\} \{\{b\},\{c\},\{a,b\},\{a,b,c\}\}} Filter chain \#11 and its STRT spectrum Filter chain \# 12 and its STRT spectrum Filter chain \# 13 and its STRT spectrum  {\ref \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c \}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c \}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} F2 \{\{a\},\{b\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{c\}\} F6 \{\{b\},\{a,b\},\{a,c\},\{b,c\},\{a, b,c\}\} \{\{b\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{a\},\{c\}\} \{\{a\},\{b\},\{c\}\} F11 \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c\}\} \{\{a,b\},\{a,c\},\{b,c\},\{a,b ,c\}\} \{\{a\},\{b\}\} \{\{b\},\{c\}\} F14 \{\{a,c\},\{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c \},\{b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} F16 \{\{a,c\},\{a,b,c\}\} \{\{a\},\{b\},\{a,b\},\{b,c\}\} \{\{a\},\{b\},\{a,b\},\{a,c\},\{b ,c\},\{a,b,c\}\} \{\{c\},\{a,b,c\}\} F18 \{\{a,b,c\}\} \{\{b\},\{a,b\},\{a,c\},\{b,c\}\} \{\{a\},\{c\},\{a,c\},\{b,c\}\} \{\{a\},\{b\},\{c\},\{a,c\},\{b,c\}, \{a,b,c\}\} -\{?\} \{\{a,b\},\{a,c\},\{b,c\},\{a,b ,c\}\} \{\{a\},\{b\},\{a,c\},\{a,b,c\}\} \{\{b\},\{c\},\{b,c\},\{a,b,c\}\} F1 \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c \}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a, c\}, \{b,c\},\{a,b,c\}\} F2 \{\{a\},\{b\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{c\}\} F6 \{\{b\},\{a,b\},\{a,c\},\{b,c\},\{a ,b,c\}\} \{\{b\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{a\},\{c\}\} \{\{a\},\{b\},\{c\}\} F11 \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c \}\} \{\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{a\},\{b\}\} \{\{b\},\{c\}\} F13 \{\{a,b\},\{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\},\{b, c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a, c\}, \{b,c\},\{a,b}   {\ref F1 \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c \}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a, c\}, \{b,c\},\{a,b,c\}\} F2 \{\{a\},\{b\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{c\}\} F6 \{\{b\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{b\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{a\},\{c\}\} \{\{a\},\{b\},\{c\}\} F11 \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c\} \} \{\{a,b\},\{a,c\},\{b,c\},\{a,b, c\}\} \{\{a\},\{b\}\} \{\{b\},\{c\}\} F13 \{\{a,b\},\{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\},\{b,c \}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a, c\}, \{b,c\},\{a,b,c\}\} F17 \{\{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{a,b\},\{a,c\}\} \{\{a\},\{b\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{c\},\{a,b,c\}\} F18 \{\{a,b,c\}\} \{\{b\},\{a,b\},\{a,c\},\{b,c\}\} \{\{a\},\{c\},\{a,b\},\{b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{b, c\}, \{a,b,c\}\} -\{?\} \{\{a,b\},\{a,c\},\{b,c\},\{a,b, c\}\} \{\{a\},\{b\},\{b,c\},\{a,b,c\}\} \{\{b\},\{c\},\{a,b\},\{a,b,}   {\ref F1 \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\} , \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\} , \{b,c\},\{a,b,c\}\} F2 \{\{a\},\{b\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{c\}\} F6 \{\{b\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{b\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{a\},\{c\}\} \{\{a\},\{b\},\{c\}\} F11 \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c\} \} \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c\} \} \{\{a\},\{b\}\} \{\{b\},\{c\}\} F14 \{\{a,c\},\{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\} ,\{b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\} , \{b,c\},\{a,b,c\}\} F17 \{\{b,c\},\{a,b}   {\ref \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c \}, \{b,c\},\{a,b,c\}\} F3 \{\{a\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,}   {\ref F1 \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a, c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} F3 \{\{a\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{b\}\} F5 \{\{a\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{a\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{b\},\{c\}\} \{\{a\},\{b\},\{c\}\} F11 \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c\} \} \{\{a,b\},\{a,c\},\{b,c\},\{a,b ,c\}\} \{\{a\},\{c\}\} \{\{a\},\{b\}\} F12 \{\{a,b\},\{a,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\},\{b, c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} F15 \{\{a,b\},\{a,b,c\}\} \{\{a\},\{c\},\{a,c\},\{b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{b\},\{a,b,c\}\} F18 \{\{a,b,c\}\} \{\{a\},\{a,b\},\{a,c\},\{b,c\} \} \{\{b\},\{c\},\{a,b\},\{a,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{a,b,c\}\} -\{?\} \{\{a,b\},\{a,c\},\{b,c\},\{a,b ,c\}\} \{\{a\},\{c\},\{a,b\},\{a,b,c\}\} \{\{a\},\{b\},\{a,c\},\{a,b,c\}\}} Filter chain \# 20 and its STRT spectrum   {\ref \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} F3 \{\{a\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{b\}\} F5 \{\{a\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{a\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{b\},\{c\}\} \{\{b\},\{c\},\{b,c\}\} F8 \{\{a\},\{a,b\},\{a,c\},\{a,b,c\}\} \{\{a\},\{a,b\},\{a,c\},\{a,b,c\}\} \{\{c\},\{b,c\}\} \{\{b\},\{b,c\}\} F12 \{\{a,b\},\{a,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\},\{ b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} F15 \{\{a,b\},\{a,b,c\}\} \{\{a\},\{c\},\{a,c\},\{b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\},\{b}   {\ref \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} F4 \{\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\}\} F6 \{\{b\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{b\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{a\},\{c\}\} \{\{a\},\{b\},\{c\}\} F11 \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c\}\} \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c\}\} \{\{b\},\{c\}\} \{\{a\},\{b\}\} F13 \{\{a,b\},\{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} F17 \{\{b,c\},\{a,b,c\}\} \{\{b\},\{c\},\{a,b\},\{a,c\}\} \{\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{a,b,c\}\} F18 \{\{a,b,c\}\} \{\{b\},\{a,b\},\{a,c\},\{b,c\}\} \{\{a\},\{c\},\{a,b\},\{b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{b,c\}, \{a,b,c\}\} -\{?\} \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c\}\} \{\{b\},\{c\},\{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{a,b\},\{a,b,c\}\}} Filter chain \# 37 and its STRT spectrum  {\ref \{\{a\},} {\ref \{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\} ,} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{a\},} {\ref \{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{a\},} {\ref \{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{a\},} {\ref \{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} F4 \{\{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{a\}\} F6 \{\{b\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{b\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{a\},} {\ref \{c\}\} \{\{a\},} {\ref \{b\},} {\ref \{c\}\} F11 \{\{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c \}\} \{\{b\},} {\ref \{c\}\} \{\{a\},} {\ref \{b\}\} F14 \{\{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{a\},} {\ref \{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\}\} \{\{a\},} {\ref \{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\}\} \{\{a\},} {\ref \{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} F16 \{\{a,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{b,} {\ref c\}\} \{\{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{a\},} {\ref \{a,} {\ref b,} {\ref c\}\} F18 \{\{a,} {\ref b,} {\ref c\}\} \{\{b\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\}\} \{\{a\},} {\ref \{c\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\}\} \{\{a\},} {\ref \{b\},} {\ref \{c\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\} ,} {\ref \{a,} {\ref b,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c \}\} \{\{b\},} {\ref \{c\},} {\ref \{a,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{a\},} {\ref \{b\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} Filter chain \# 38 and its STRT spectrum F1 \{\{a\},} {\ref \{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{a\},} {\ref \{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{a\},} {\ref \{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{a\},} {\ref \{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} F4 \{\{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{a\}\} F6 \{\{b\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{b\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{a\},} {\ref \{c\}\} \{\{a\},} {\ref \{b\},} {\ref \{c\}\} F11 \{\{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{b\},} {\ref \{c\}\} \{\{a\},} {\ref \{b\}\} F14 \{\{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{a\},} {\ref \{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\}\} \{\{a\},} {\ref \{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\}\} \{\{a\},} {\ref \{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} F17 \{\{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\}\} \{\{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{a\},} {\ref \{a,} {\ref b,} {\ref c\}\} F18 \{\{a,} {\ref b,} {\ref c\}\} \{\{b\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\}\} \{\{a\},} {\ref \{c\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\}\} \{\{a\},} {\ref \{b\},} {\ref \{c\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{b\},} {\ref \{c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{a\},} {\ref \{b\},} {\ref \{a,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\}} Global Journal of Computer Science and Technology 
\section[{F1}]{F1}F1F1\par
Volume XX Issue I Version I 69 Year 2020 
\section[{( ) D}]{( ) D}\par
Filter chain \# 39 and its STRT spectrum  {\ref \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} F4 \{\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\}\} F6 \{\{b\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{b\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{a\},\{c\}\} \{\{a\},\{c\},\{a,c\}\} F9 \{\{b\},\{a,b\},\{b,c\},\{a,b,c\}\} \{\{b\},\{a,b\},\{b,c\},\{a,b,c\}\} \{\{c\},\{a,c\}\} \{\{a\},\{a,c\}\} F13 \{\{a,b\},\{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,c\}\} \{\{a\},\{b\},\{c\},\{a,b\}, \{a,c\},\{b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} F15 \{\{a,b\},\{a,b,c\}\} \{\{b\},\{c\},\{a,c\},\{b,c\}\} \{\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{a,b,c\}\} F18 \{\{a,b,c\}\} \{\{b\},\{a,b\},\{a,c\},\{b,c\}\} \{\{a\},\{c\},\{a,b\},\{b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} -\{?\} \{\{b\},\{a,b\},\{b,c\},\{a,b,c\}\} \{\{c\},\{a,b\},\{a,c\},\{a,b,c\}\} \{\{a\},\{a,c\},\{b,c\},\{a,b,c\}\}} Filter chain \#40 and its STRT spectrum Filter chain \# 41 and its STRT spectrum  {\ref \{\{a\},} {\ref \{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{a\},} {\ref \{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{a\},} {\ref \{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{a\},} {\ref \{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} F4 \{\{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{a\}\} F7 \{\{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{a\},} {\ref \{b\}\} \{\{a\},} {\ref \{b\},} {\ref \{c\}\} F11 \{\{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{b\},} {\ref \{c\}\} \{\{a\},} {\ref \{c\}\} F12 \{\{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{a\},} {\ref \{b\},} {\ref \{c\},} {\ref \{b,} {\ref c\}\} \{\{a\},} {\ref \{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\}\} \{\{a\},} {\ref \{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} F15 \{\{a,} {\ref b\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{b\},} {\ref \{c\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\}\} \{\{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{a\},} {\ref \{a,} {\ref b,} {\ref c\}\} F18 \{\{a,} {\ref b,} {\ref c\}\} \{\{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\}\} \{\{a\},} {\ref \{b\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\}\} \{\{a\},} {\ref \{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{a\},} {\ref \{c\},} {\ref \{a,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} Filter chain \# 42 and its STRT spectrum F1 \{\{a\},} {\ref \{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{a\},} {\ref \{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{a\},} {\ref \{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{a\},} {\ref \{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} F4 \{\{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b,} {\ref c\}\} \{\{b\},} {\ref \{c\},} {\ref \{a,} {\ref b\},} {\ref \{a,} {\ref c\},} {\ref \{b,} {\ref c\},} {\ref \{a,} {\ref b}   {\ref F12 \{\{a,b\},\{a,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} F16 \{\{a,c\},\{a,b,c\}\} \{\{b\},\{c\},\{a,b\},\{b,c\}\} \{\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{a,b,c\}\} F18 \{\{a,b,c\}\} \{\{c\},\{a,b\},\{a,c\},\{b,c\}\} \{\{a\},\{b\},\{a,b\},\{a,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{a,b,c\}\} -\{?\} \{\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{b\},\{c\},\{a,c\},\{a,b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,b,c\}\}} Filter chain \# 43 and its STRT spectrum  {\ref \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} F4 \{\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,}   {\ref F7 \{\{c\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{c\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{a\},\{b\}\} \{\{a\},\{b\},\{c\}\} F11 \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c\}\} \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c\}\} \{\{b\},\{c\}\} \{\{a\},\{c\}\} F13 \{\{a,b\},\{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} F17 \{\{b,c\},\{a,b,c\}\} \{\{b\},\{c\},\{a,b\},\{a,c\}\} \{\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{a,b,c\}\} F18 \{\{a,b,c\}\} \{\{c\},\{a,b\},\{a,c\},\{b,c\}\} \{\{a\},\{b\},\{a,b\},\{b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{b,c\}, \{a,b,c\}\} -\{?\} \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c\}\} \{\{b\},\{c\},\{b,c\},\{a,b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,b,c\}\}} Filter chain \# 45 and its STRT spectrum  {\ref \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} F4 \{\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\}\} F7 \{\{c\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{c\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{a\},\{b\}\} \{\{a\},\{b\},\{c\}\} F11 \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c\}\} \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c\}\} \{\{b\},\{c\}\} \{\{a\},\{c\}\} F14 \{\{a,c\},\{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} F16 \{\{a,c\},\{a,b,c\}\} \{\{b\},\{c\},\{a,b\},\{b,c\}\} \{\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{a,b,c\}\} F18 \{\{a,b,c\}\} \{\{c\},\{a,b\},\{a,c\},\{b,c\}\} \{\{a\},\{b\},\{a,c\},\{b,c\}\} \{\{a\},\{b\},\{c\},\{a,c\},\{b,c\}, \{a,b,c\}\} -\{?\} \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c\}\} \{\{b\},\{c\},\{a,c\},\{a,b,c\}\} \{\{a\},\{c\},\{b,c\},\{a,b,c\}\}} Global Journal of Computer Science and TechnologyF1F1F1F1\par
Volume XX Issue I Version I 71 Year 2020 
\section[{( ) D}]{( ) D}\par
Filter chain \# 46 and its STRT spectrum  {\ref \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} F4 \{\{b\},\{c\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\}\} F7 \{\{c\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{c\},\{a,b\},\{a,c\},\{b,c\}, \{a,b}   {\ref ,\{a\},\{b\},\{c\},\{d\},\{a,b\},\{a,c\}, \{a,d\},\{b,c\},\{b,d\}, \{c,d\}, \{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\}, \{a,b,c,d\}\}.} One can construct a filter set F whose elements satisfy the following property: 'Any element of F ensures the presence of all its super sets present in the power set of X. One can construct 166 topological filters from the ground set X = \{a,b,c,d\}. This list is given in table 2.F1 
\section[{F1}]{F1}\par
\{\{a\}  {\ref ,\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} F4 \{\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{b\},\{c\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\}\} F7 \{\{c\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{c\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{a\},\{b\}\} \{\{a\},\{b\},\{a,b\}\} F10 \{\{c\},\{a,c\},\{b,c\},\{a,b,c\}\} \{\{c\},\{a,c\},\{b,c\},\{a,b,c\}\} \{\{b\},\{a,b\}\} \{\{a\},\{a,b\}\} F14 \{\{a,c\},\{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} F16 \{\{a,c\},\{a,b,c\}\} \{\{b\},\{c\},\{a,b\},\{b,c\}\} \{\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{a,b,c\}\} F18 \{\{a,b,c\}\} \{\{c\},\{a,b\},\{a,c\},\{b,c\}\} \{\{a\},\{b\},\{a,c\},\{b,c\}\} \{\{a\},\{b\},\{a,b\},\{a,c\}, \{b,c\}, \{a,b,c\}\} -\{?\} \{\{c\},\{a,c\},\{b,c\},\{a,b,c\}\} \{\{b\},\{a,b\},\{a,c\},\{a,b,c\}\} \{\{a\},\{a,b\},\{b,c\},\{a,b,c\}\} F1 \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} F4 \{\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\}\} F7 \{\{c\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{c\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{a\},\{b\}\} \{\{a\},\{b\},\{a,b\}\} F10 \{\{c\},\{a,c\},\{b,c\},\{a,b,c\}\} \{\{c\},\{a,c\},\{b,c\},\{a,b,c\}\} \{\{b\},\{a,b\}\} \{\{a\},\{a,b\}\} F14 \{\{a,c\},\{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} F17 \{\{b,c\},\{a,b,c\}\} \{\{b\},\{c\},\{a,b\},\{a,c\}\} \{\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{a,b,c\}\} F18 \{\{a,b,c\}\} \{\{c\},\{a,b\},\{a,c\},\{b,c\}\} \{\{a\},\{b\},\{a,c\},\{b,c\}\} \{\{a\},\{b\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} -\{?\} \{\{c\},\{a,c\},\{b,c\},\{a,b,c\}\} \{\{b\},\{a,b\},\{b,c\},\{a,b,c\}\} \{\{a\},\{a,b\},\{a,c\},\{a,b,c\}\}}    {\ref F1 \{\{a\},\{b\},\{c\},\{d\},\{a,b\},\{a,c\},\{a,d\},\{b,c\},\{b,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\}, \{a,b,c,d\}\} 15 F2 \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\},\{a,d\},\{b,c\},\{b,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 14 F3 \{\{a\},\{b\},\{d\},\{a,b\},\{a,c\},\{a,d\},\{b,c\},\{b,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 14 F4 \{\{a\},\{c\},\{d\},\{a,b\},\{a,c\},\{a,d\},\{b,c\},\{b,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 14 F5 \{\{b\},\{c\},\{d\},\{a,b\},\{a,c\},\{a,d\},\{b,c\},\{b,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 14 F6 \{\{a\},\{b\},\{a,b\},\{a,c\},\{a,d\},\{b,c\},\{b,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 13 F7 \{\{a\},\{c\},\{a,b\},\{a,c\},\{a,d\},\{b,c\},\{b,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 13 F8 \{\{b\},\{c\},\{a,b\},\{a,c\},\{a,d\},\{b,c\},\{b,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 13 F9 \{\{a\},\{d\},\{a,b\},\{a,c\},\{a,d\},\{b,c\},\{b,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 13 F10 \{\{b\},\{d\},\{a,b\},\{a,c\},\{a,d\},\{b,c\},\{b,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 13 F11 \{\{c\},\{d\},\{a,b\},\{a,c\},\{a,d\},\{b,c\},\{b,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 13 F12 \{\{a\},\{b\},\{a,b\},\{a,c\},\{a,d\},\{b,c\},\{b,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 12 F13 \{\{a\},\{a,b\},\{a,c\},\{a,d\},\{b,c\},\{b,d\}\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 12 F14 \{\{a\},\{c\},\{a,b\},\{a,c\},\{a,d\},\{b,c\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 12 F15 \{\{b\},\{a,b\},\{a,c\},\{a,d\},\{b,c\},\{b,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 12 F16 \{\{b\},\{c\},\{a,b\},\{a,c\},\{b,c\},\{b,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 12 F17 \{\{c\},\{a,b\},\{a,c\},\{a,d\},\{b,c\},\{b,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 12 F18 \{\{a\},\{d\},\{a,b\},\{a,c\},\{a,d\},\{b,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 12 F19 \{\{d\},\{a,b\},\{a,c\},\{a,d\},\{b,c\},\{b,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 12 F20 \{\{b\},\{d\},\{a,b\},\{a,d\},\{b,c\},\{b,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 12 F21 \{\{c\},\{d\},\{a,c\},\{a,d\},\{b,c\},\{b,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 12 F35 \{\{a\},\{a,b\},\{a,c\},\{a,d\},\{b,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 10 F36 \{\{a\},\{a,b\},\{a,c\},\{a,d\},\{b,c\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 10 F37 \{\{a\},\{a,b\},\{a,c\},\{a,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 10 F38 \{\{b\},\{a,b\},\{b,c\},\{b,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 10 F39 \{\{b\},\{a,b\},\{a,d\},\{b,c\},\{b,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 10 F40 \{\{b\},\{a,b\},\{a,c\},\{b,c\},\{b,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 10 F41 \{\{a,c\},\{a,d\},\{b,c\},\{b,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 10 F42 \{\{a,b\},\{a,d\},\{b,c\},\{b,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 10 F43 \{\{a,b\},\{a,c\},\{b,c\},b,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 10 F44 \{\{a,b\},\{a,c\},\{a,d\},\{b,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 10 F45 \{\{a,b\},\{a,c\},\{a,d\},\{b,c\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 10 F46 \{\{a,b\},\{a,c\},\{a,d\},\{b,c\},\{b,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 10 F47 \{\{c,\},\{a,c\},\{b,c\},\{b,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 10 F48 \{\{c\},\{a,c\},\{a,d\},\{b,c\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 10 F49 \{\{c\},\{a,b\},\{a,c\},\{b,c\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 10 F50 \{\{d\},\{a,c\},\{a,d\},\{b,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 10 F51 \{\{d\},\{a,d\},\{b,c\},\{b,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 10 F52 \{\{d\},\{a,b\},\{a,d\},\{b,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 10 F53 \{\{a\},\{a,b\},\{a,c\},\{a,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 9 F54 \{\{b\},\{a,b\},\{b,c\},\{b,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 9 F55 \{\{a,d\},\{b,c\},\{b,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 9 F56 \{\{a,d\},\{b,c\},\{b,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 9} Year 2020 ( ) D  {\ref \{\{a,c\},\{a,d\},\{b,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 9 F58 \{\{a,c\},\{a,d\},\{b,c\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 9 F59 \{\{a,c\},\{a,d\},\{b,c\},\{b,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 9 F60 \{\{a,b\},\{b,c\},\{b,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 9 F61 \{\{a,b\},\{a,d\},\{b,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 9 F62 \{\{a,b\},\{a,d\},\{b,c\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 9 F63 \{\{a,b\},\{a,d\},\{b,c\},\{b,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 9 F64 \{\{a,b\},\{a,c\},\{b,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 9 F65 \{\{a,b\},\{a,c\},\{b,c\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 9 F66 \{\{a,b\},\{a,c\},\{b,c\},\{b,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 9 F67 \{\{a,b\},\{a,c\},\{a,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 9 F68 \{\{a,b\},\{a,c\},\{a,d\},\{b,c\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 9 F69 \{\{a,b\},\{a,c\},\{a,d\},\{b,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 9 F70 \{\{c\},\{a,c\},\{b,c\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 9 F71 \{\{d\},\{a,d\},\{b,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 9 F72 \{\{a\},\{a,b\},\{a,c\},\{a,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{a,b,c,d\}\} 8 F73 \{\{b\},\{a,b\},\{b,c\},\{b,d\},\{a,b,c\},\{a,b,d\},\{b,c,d\},\{a,b,c,d\}\} 8 F74 \{\{b,c\},\{b,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 8 F75 \{\{a,d\},\{b,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 8 F76 \{\{a,d\},\{b,c\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 8 F77 \{\{a,d\},\{b,c\},\{b,d\} ,\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 8 F78 \{\{a,c\},\{b,c\},\{b,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 8 F79 \{\{a,c\},\{b,c\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 8 F80 \{\{a,c\},\{a,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 8 F81 \{\{a,c\},\{a,d\},\{b,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 8 F82 \{\{a,c\},\{a,d\},\{b,c\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 8 F83 \{\{a,b\},\{b,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 8 F84 \{\{a,b\},\{b,c\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 8 F85 \{\{a,b\},\{b,c\},\{b,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 8 F86 \{\{a,b\},\{a,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 8 F87 \{\{a,b\},\{a,d\},\{b,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 8 F88 \{\{a,b\},\{a,d\},\{b,c\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 8 F89 \{\{a,c\},\{b,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 8 F90 \{\{a.b\},\{a,c\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 8 F91 \{\{a,b\},\{a,c\},\{b,d\} ,\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 8 F92 \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 8 F93 \{\{a,b\},\{a,c\},\{a,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 8 F94 \{\{c\},\{a,c\},\{b,c\},\{c,d\},\{a,b,c\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 8 F95 \{\{d\},\{a,d\},\{b,d\},\{c,d\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 8 F96 \{\{a,d\},\{b,d\},\{c,d\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 7 F97 \{\{a,c\},\{b,c\},\{c,d\},\{a,b,c\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 7 F98 \{\{b,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 7 F99 \{\{b,c\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 7 F100 \{\{b,c\},\{b,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 7 F101 \{\{a,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 7 F102 \{\{a,d\},\{b,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 7 F103 \{\{a,d\},\{b,c\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 7 F104 \{\{a,c\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 7 F105 \{\{a,c\},\{b,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 7 F106 \{\{a,c\},\{b,c\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 7 F107 \{\{a,c\},\{a,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 7 F108 \{\{a,b\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 7 F109 \{\{a,b\},\{b,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 7 F110 \{\{a,b\},\{b,c\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 7 F111 \{\{a,b\},\{a,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 7 F112 \{\{a,b\},\{a,c\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 7 F113 \{\{a,b\},\{b,c\},\{b,d\},\{a,b,c\},\{a,b,d\},\{b,c,d\},\{a,b,c,d\}\} 7 F114 \{\{a,b\},\{a,c\},\{a,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{a,b,c,d\}\} 7 F115 \{\{b,d\},\{c,d\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 6 F116 \{\{b,c\},\{c,d\},\{a,b,c\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 6 F117 \{\{b,c\},\{b,d\},\{a,b,c\},\{a,b,d\},\{b,c,d\},\{a,b,c,d\}\} 6 F118 \{\{a,d\},\{c,d\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 6 F119 \{\{a,d\},\{b,d\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 6 F120 \{\{a,c\},\{c,d\},\{a,b,c\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 6 F121 \{\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 6 F122 \{\{b,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 6 F123 \{\{b,c\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 6 F124 \{\{a,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 6 F125 \{\{a,c\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 6 F126 \{\{a,b\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 6 F127 \{\{a,c\},\{b,c\},\{a,b,c\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 6 F128 \{\{a,c\},\{a,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{a,b,c,d\}\} 6 F129 \{\{a,b\},\{b,d\},\{a,b,c\},\{a,b,d\},\{b,c,d\},\{a,b,c,d\}\} 6 F130 \{\{a,b\},\{b,c\},\{a,b,c\},\{a,b,d\},\{b,c,d\},\{a,b,c,d\}\} 6 F131 \{\{a,b\},\{a,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{a,b,c,d\}\} 6 F132 \{\{a,b\},\{a,c\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{a,b,c,d\}\} 6 F133 \{\{b,d\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 5 F134 \{\{c,d\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 5 F135 \{\{c,d\},\{a,b,c\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 5 F136 \{\{b,d\},\{a,b,c\},\{a,b,d\},\{b,c,d\},\{a,b,c,d\}\} 5 F137 \{\{b,c\},\{a,b,c\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 5 F138 \{\{b,c\},\{a,b,c\},\{a,b,d\},\{b,c,d\},\{a,b,c,d\}\} 5 F139 \{\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 5 F140 \{\{a,d\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 5 F141 \{\{a,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{a,b,c,d\}\} 5 F142 \{\{a,c\},\{a,b,c\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 5 F143 \{\{a,c\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{a,b,c,d\}\} 5 F144 \{\{a,b\},\{a,b,c\},\{a,b,d\},\{b,c,d\},\{a,b,c,d\}\} 5 F145 \{\{a,b\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{a,b,c,d\}\} 5 F146 \{\{b,d\},\{a,b,d\},\{b,c,d\},\{a,b,c,d\}\} 4 F147 \{\{c,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 4 F148 \{\{b,c\},\{a,b,c\},\{b,c,d\},\{a,b,c,d\}\} 4 F149 \{\{a,b,c\},\{a,b,d\},\{a,c,d\},\{a,b,c,d\}\} 4 F150 \{\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 4 F151 \{\{a,b,c\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 4 F152 \{\{a,b,c\},\{a,b,d\},\{b,c,d\},\{a,b,c,d\}\} 4 F153 \{\{a,d\},\{a,b,d\},\{a,c,d\},\{a,b,c,d\}\} 4 F154 \{\{a,c\},\{a,b,c\},\{a,c,d\},\{a,b,c,d\}\} 4 F155 \{\{a,b\},\{a,b,c\},\{a,b,d\},\{a,b,c,d\}\} 4 F156 \{\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 3 F157 \{\{a,b,d\},\{a,c,d\},\{a,b,c,d\}\} 3 F158 \{\{a,b,d\},\{b,c,d\},\{a,b,c,d\}\} 3 F159 \{\{a,b,c\},\{a,c,d\},\{a,b,c,d\}\} 3 F160 \{\{a,b,c\},\{b,c,d\},\{a,b,c,d\}\} 3 F161 \{\{a,b,c\},\{a,b,d\},\{a,b,c,d\}\} 3 F162 \{\{a,c,d\},\{a,b,c,d\}\} 2 F163 \{\{b,c,d\},\{a,b,c,d\}\} 2 F164 \{\{a,b,d\},\{a,b,c,d\}\} 2 F165 \{\{a,b,c\},\{a,b,c,d\}\} 2 F166 (\{a,b,c,d\}\} 1} The lattice <?, ?> is constructed as given in Fig.  {\ref 3} whose elements are 166 topological filters defined over the ground set X = \{a,b,c,d\}. Note that the symbol ? denotes the partial order relation of 'subset of'. One can enumerate 13,767 linear maximal filter chains from this lattice. One can compute STRT spectra for all the 13,767 linear maximal filter chains. For example, one linear maximal filter chain is considered here and its STRT shown in table  {\ref 3}.  
\section[{F57}]{F57} 
\section[{Observations}]{Observations}\par
By applying STRT to the above maximal filter chains, we examined few pair-wise intersection properties. The level with filter of maximum cardinality is considered as Level1.By taking two random filter chains, which deviate at certain levels the following properties were observed:\par
Deviation in any combination of even levels results in following properties:\par
Union of spectra of two filter chains is same as Spectrum of Intersection of those two filter chains.\par
Intersection of spectra of two filter chains is same as Spectrum of Union of those two filter chains.\par
One can easily verify these properties by applying STRT to the below pair of filter chains: For example, let us consider n=3, Deviation in Level 2-F1-F2-F5-F8-F12-F15-F18 F1-F3-F5-F8-F12-F15-F18 Deviation in Level 4-F1-F3-F5-F8-F12-F15-F18 F1-F3-F5-F11-F12-F15-F18 Deviation in Level 6-F1-F4-F7-F10-F14-F16-F18 F1-F4-F7-F10-F14-F17-F18 Deviation in Level 4 and 6-F1-F2-F5-F8-F12-F15-F18 F1-F2-F5-F11-F12-F16-F18 
\section[{Deviation in any combination of odd levels results in following properties:}]{Deviation in any combination of odd levels results in following properties:}\par
Union of spectra of two filter chains is same as Spectrum of Union of those two filter chains.\par
Intersection of spectra of two filter chains is same as Spectrum of Intersection of those two filter chains.\par
One can easily verify these properties by applying STRT to the below pair of filter chains: Deviation in Level 3-F1-F3-F5-F11-F12-F15-F18 F1-F3-F7-F11-F12-F15-F18\par
Deviation in Level 5-F1-F2-F5-F11-F12-F16-F18 F1-F2-F5-F11-F14-F16-F18\par
Deviation in Level 3 and 5-F1-F3-F5-F11-F12-F15-F18 F1-F3-F7-F11-F13-F15-F18\par
V. 
\section[{Concluding Remarks}]{Concluding Remarks}\par
All orthogonal transforms, be it continuous or discrete, are models of first order logic, that is, they have been developed in the framework of first order logic that deal with elements of sets. Alternatively, STRT is a novel concept developed in the framework of second order logic that deals with set of sets, and so it has potential applications to solve problems related to functions of sets.\begin{figure}[htbp]
\noindent\textbf{2}\includegraphics[]{image-2.png}
\caption{\label{fig_0}Fig. 2 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-3.png}
\caption{\label{fig_1}F1}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-4.png}
\caption{\label{figure4}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2} \par 
\begin{longtable}{}
\end{longtable} \par
 
\caption{\label{tab_0}Table 2 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{} \par 
\begin{longtable}{P{0.8435129509713228\textwidth}P{0.0006388760407030527\textwidth}P{0.0016217622571692877\textwidth}P{0.0018183395004625347\textwidth}P{0.0024080712303422755\textwidth}}
\multicolumn{5}{l}{,c\} \{\{a\},\{a63 , \{a,b,c\}\} \{\{b\},\{a,b,c\}\} \{\{a\},\{a,b\},\{a,c\},\{b,c\}\} \{\{b\},\{c\},\{a,b\},\{a,c\}\} \{\{b\},\{c\},\{a,b\},\{b,c\},\{a,c\} , \{a,b,c\}\} Year 2020 ( ) D Filter chain \# 21 and its STRT spectrum F18 \{\{a,b,c\}\} -\{?\} F1 \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} F3 \{\{a\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{b\}\} F5 \{\{a\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{a\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{b\},\{c\}\} \{\{a\},\{b\},\{c\}\} F11 \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c\} \} \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c\} \} \{\{a\},\{c\}\} \{\{a\},\{b\}\} c\}, \{a,b,c\}\} \{\{b\},\{a,b,c\}\} F18 \{\{a,b,c\}\} \{\{a\},\{a,b\},\{a,c\},\{b,c\}\} \{\{b\},\{c\},\{a,b\},\{b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{b,c\}, \{a,b,c\}\} -\{?\} \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c\} \} \{\{a\},\{c\},\{a,b\},\{a,b,c\}\} \{\{a\},\{b\},\{b,c\},\{a,b,c\}\} Filter chain \# 22 and its STRT spectrum F1 \{\{a\},\{b\},\{c\},\{a,b\},\{a,c \}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c \}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} F3 \{\{a\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{b\}\} F5 \{\{a\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{a\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{b\},\{c\}\} \{\{a\},\{b\},\{c\}\} F11 \{\{a,b\},\{a,c\},\{b,c\},\{a,b, c\}\} \{\{a,b\},\{a,c\},\{b,c\},\{a,b, c\}\} \{\{a\},\{c\}\} \{\{a\},\{b\}\} F13 \{\{a,b\},\{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\},\{b,c \}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} F17 \{\{b,c\},\{a,b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{b\},\{a,b,c\}\} F18 \{\{a,b,c\}\} \{\{a\},\{a,b\},\{a,c\},\{b,c\}\} \{\{b\},\{c\},\{a,b\},\{b,c\}\} \{\{a\},\{b\},\{c\},\{a.b\},\{b,c\}, \{a,b,c\}\} -\{?\} \{\{a,b\},\{a,c\},\{b,c\},\{a,b, c\}\} \{\{a\},\{c\},\{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{a,b\},\{a,b,c\}\} Filter chain \# 23 and its STRT spectrum F3 \{\{a\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\},\{b,c \}, \{a,b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\},\{b,c \}, \{a,b,c\}\} \{\{b\}\} F5 \{\{a\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{a\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{b\},\{c\}\} \{\{a\},\{b\},\{c\}\} F11 \{\{a,b\},\{a,c\},\{b,c\},\{a,b, c\}\} \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c \}\} \{\{a\},\{c\}\} \{\{a\},\{b\}\} F12 \{\{a,b\},\{a,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} F16 \{\{a,c\},\{a,b,c\}\} \{\{a\},\{c\},\{a,b\},\{b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\},\{b,c \}, \{a,b,c\}\} \{\{b\},\{a,b,c\}\} F18 \{\{a,b,c\}\} \{\{a\},\{a,b\},\{a,c\},\{b,c\}\} \{\{b\},\{c\},\{a,b\},\{a,c\}\} \{\{a\},\{b\},\{c\},\{a.b\},\{a,c\}, \{a,b,c\}\} -\{?\} \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c \}\} \{\{a\},\{c\},\{a,c\},\{a,b,c\}\} \{\{a\},\{b\},\{a,b\},\{a,b,c\}\} F5 \{\{a\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{a\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{b\},\{c\}\} \{\{a\},\{b\},\{c\}\} F11 \{\{a,b\},\{a,c\},\{b,c\},\{a,b, c\}\} \{\{a,b\},\{a,c\},\{b,c\},\{a,b, c\}\} \{\{a\},\{c\}\} \{\{a\},\{b\}\} F14 \{\{a,c\},\{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\},\{b,c \}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} F16 \{\{a,c\},\{a,b,c\}\} \{\{a\},\{c\},\{a,b\},\{b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{b\},\{a,b,c\}\} F18 \{\{a,b,c\}\} \{\{a\},\{a,b\},\{a,c\},\{b,c\}\} \{\{b\},\{c\},\{a,c\},\{b,c\}\} \{\{a\},\{b\},\{c\},\{a,c\},\{b,c\}, \{a,b,c\}\} -\{?\} \{\{a,b\},\{a,c\},\{b,c\},\{a,b, c\}\} \{\{a\},\{c\},\{a,c\},\{a,b,c\}\} \{\{a\},\{b\},\{b,c\},\{a,b,c\}\} Filter chain \# 24 and its STRT spectrum F1 \{\{a\},\{b\},\{c\},\{a,b\},\{a,c \}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\} , \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} F3 \{\{a\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{b\}\} F5 \{\{a\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{a\},\{a,b\},\{a,c\},\{b,c\},\{ a,b,c\}\} \{\{b\},\{c\}\} \{\{a\},\{b\},\{c\}\} F11 \{\{a,b\},\{a,c\},\{b,c\},\{a,b, c\}\} \{\{a,b\},\{a,c\},\{b,c\},\{a,b, c\}\} \{\{a\},\{c\}\} \{\{a\},\{b\}\} F14 \{\{a,c\},\{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\},\{b,c \}\} c\}, \{a,b,c\}\} -\{?\} \{\{a,b\},\{a,c\},\{b,c\},\{a,b, c\}\} \{\{a\},\{c\},\{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{a,c\},\{a,b,c\}\} Filter chain \# 25 and its STRT spectrum F1 \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} F3 \{\{a\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{b\}\} F7 \{\{c\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{c\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{a\},\{b\}\} \{\{a\},\{b\},\{c\}\} F11 \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c\}\} \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c\}\} \{\{a\},\{c\}\} \{\{b\},\{c\}\} F12 \{\{a,b\},\{a,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} F15 \{\{a,b\},\{a,b,c\}\} \{\{a\},\{c\},\{a,c\},\{b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{b\},\{a,b,c\}\} F18 \{\{a,b,c\}\} \{\{c\},\{a,b\},\{a,c\},\{b,c\}\} \{\{a\},\{b\},\{a,b\},\{a,c\}\} \{\{a\},\{b\},\{c\},\{a,b\}, \{a,c\},\{a,b,c\}\} -\{?\} \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,b,c\}\} \{\{b\},\{c\},\{a,c\},\{a,b,c\}\} Filter chain \# 26 and its STRT spectrum Global Journal of Computer Science and Technology Volume XX Issue I Version I 65 Year 2020 ( ) D F7 \{\{c\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{c\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{a\},\{b\}\} \{\{a\},\{b\},\{c\}\} F11 \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c\}\} \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c\}\} \{\{a\},\{c\}\} \{\{b\},\{c\}\} F12 \{\{a,b\},\{a,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} F16 \{\{a,c\},\{a,b,c\}\} \{\{a\},\{c\},\{a,b\},\{b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{b\},\{a,b,c\}\} F18 \{\{a,b,c\}\} \{\{c\},\{a,b\},\{a,c\},\{b,c\}\} \{\{a\},\{b\},\{a,b\},\{a,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{a,b,c\}\} -\{?\} \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c\}\} \{\{a\},\{c\},\{a,c\},\{a,b,c\}\} \{\{b\},\{c\},\{a,b\},\{a,b,c\}\} Filter chain \# 27 and its STRT spectrum F1 \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\}, \{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} F3 \{\{a\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{b\}\} F7 \{\{c\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{c\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{a\},\{b\}\} \{\{a\},\{b\},\{c\}\} F11 \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c\} \} \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c\} \} \{\{a\},\{c\}\} \{\{b\},\{c\}\} F13 \{\{a,b\},\{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} F15 \{\{a,b\},\{a,b,c\}\} \{\{a\},\{c\},\{a,c\},\{b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{b\},\{a,b,c\}\} F18 \{\{a,b,c\}\} \{\{c\},\{a,b\},\{a,c\},\{b,c\}\} \{\{a\},\{b\},\{a,b\},\{b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{b,c\}, \{a,b,c\}\} -\{?\} \{\{a,b\}c\}, \{b,c\},\{a,b,c\}\} F3 \{\{a\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{b\}\} F7 \{\{c\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{c\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{a\},\{b\}\} \{\{a\},\{b\},\{c\}\} F11 \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c\}\} \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c\}\} \{\{a\},\{c\}\} \{\{b\},\{c\}\} F13 \{\{a,b\},\{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} F17 \{\{b,c\},\{a,b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{b\},\{a,b,c\}\} F18 \{\{a,b,c\}\} \{\{c\},\{a,b\},\{a,c\},\{b,c\}\} \{\{a\},\{b\},\{a,b\},\{b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{b,c\}, \{a,b,c\}\} -\{?\} \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c\}\} \{\{a\},\{c\},\{b,c\},\{a,b,c\}\} \{\{b\},\{c\},\{a,b\},\{a,b,c\}\} Filter chain \# 29 and its STRT spectrum F1 \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} F3 \{\{a\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{b\}\} F7 \{\{c\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{c\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{a\},\{b\}\} \{\{a\},\{b\},\{c\}\} F11 \{a,b,c\}\} \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c\}\} \{\{a\},\{c\}\} \{\{b\},\{c\}\} F17 \{\{b,c\},\{a,b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\}\} \{a,b,c\}\} \{\{b\},\{a,b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\},\{b,c\}, \{\{a,b\},\{a,c\},\{b,c\}, F16 \{\{a,c\},\{a,b,c\}\} \{\{a\},\{c\},\{a,b\},\{b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{a,b,c\}\} \{a,b,c\}\} \{\{b\},\{a,b,c\}\} F18 \{\{a,b,c\}\} \{\{c\},\{a,b\},\{a,c\},\{b,c\}\} \{\{a\},\{b\},\{a,c\},\{b,c\}\} \{\{a\},\{b\},\{c\},\{a,c\},\{b,c\}, \{a,b,c\}\} -\{?\} -\{?\} \{\{c\},\{a,c\},\{b,c\},\{a,b,c\}\} \{\{b\},\{a,b\},\{a,c\},\{a,b,c -\{?\} \{\{a,b\},\{a,c\},\{b,c\}, \{\{b\},\{c\},\{a,b\},\{a,b,c\}\} \{\{a\},\{b\},\{b,c\},\{a,b,c\}\} \{a,b,c\}\} \{\{a\},\{a,b\},\{b,c\},\{a,b,c\}\} \}\} Filter chain \# 36 and its STRT spectrum \{\{a,b\}Filter chain \# 30 and its STRT spectrum Filter chain \# 31 and its STRT spectrum F1 \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} F3 \{\{a\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{b\}\} F7 \{\{c\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{c\},\{a,b\},\{a,c\},\{b,c\}, F10 \{\{c\},\{a,c\},\{b,c\},\{a,b,c\}\} \{\{c\},\{a,c\},\{b,c\},\{a,b,c\}\} \{\{a\},\{a,b\}\} \{\{b\},\{a,b\}\} F14 \{\{a,c\},\{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\}, \{a,b,c\}\} F16 \{\{a,c\},\{a,b,c\}\} \{\{a\},\{c\},\{a,b\},\{b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{b\},\{a,b,c\}\} F18 \{\{a,b,c\}\} \{\{c\},\{a,b\},\{a,c\},\{b,c\}\} \{\{a\},\{b\},\{a,c\},\{b,c\}\} \{\{a\},\{b\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} -\{?\} \{\{c\},\{a,c\},\{b,c\},\{a,b,c\}\} \{\{a\},\{a,b\},\{a,c\},\{a,b,c\}\} \{\{b\},\{a,b\},\{b,c\},\{a,b,c\}\} Filter chain \# 32 and its STRT spectrum F1 \{\{a\},\{b\},\{c\},\{a,b\},\{a, c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c \}, \{b,c\},\{a,b,c\}\} F3 \{\{a\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\},\{b,c\} , \{a,b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{b\}\} F7 \{\{c\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{c\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{a\},\{b\}\} \{\{a\},\{b\},\{a,b\}\} F10 \{\{c\},\{a,c\},\{b,c\},\{a,b,c \}\} \{\{c\},\{a,c\},\{b,c\},\{a,b,c\}\} \{\{a\},\{a,b\}\} F14 \{\{a,c\},\{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\},\{b,c\} \} \}, \{b,c\},\{a,b,c\}\} F11 \{\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{a,b,c\}\} \{\{b\},\{c\}\} \{\{a\},\{b\}\} \{\{a,b\},\{a,c\},\{b,c\}, \{\{a\},\{b\},\{c\},\{a,b\},\{a,c F6 \{\{b\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{b\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{a\},\{c\}\} \{\{a\},\{b\},\{c\}\} \{\{b\},\{a,b\}\} Filter chain \# 35 and its STRT spectrum F1 \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\} ,\{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} F4 \{\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\}\} F6 \{\{b\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{b\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{a\},\{c\}\} \{\{a\},\{b\},\{c\}\} F1 1 \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c\} \} \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c\} \} \{\{b\},\{c\}\} \{\{a\},\{b\}\} F1 2 \{\{a,b\},\{a,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\},\{b,c\} \} \{\{a\},\{b\},\{c\},\{a,b\}, \{a,c\}, \{b,c\},\{a,b,c\}\} F1 6 \{\{a,c\},\{a,b,c\}\} \{\{b\},\{c\},\{a,b\},\{b,c\}\} \{\{b\},\{c\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{a\},\{a,b,c\}\} F1 8 \{\{a,b,c\}\} \{\{b\},\{a,b\},\{a,c\},\{b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\}\} \{\{a\},\{b\},\{c\},\{a,b\}, \{a,c\}, \{a,b,c\}\} -\{?\} \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c\} \} \{\{b\},\{c\},\{a,c\},\{a,b,c\}\} \{\{a\},\{b\},\{a,b\},\{a,b ,c\}\} Global Journal of Computer Science and Technology ( ) D F4 \{\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} , \{a,b,c\}\} \{b,c\},\{a,b,c\}\} \{\{a\}\} \{\{b\},\{c\},\{a,b\},\{a,c\}, \{\{b\},\{c\},\{a,b\},\{a,c\},\{b,c\} \{a,b,c\}\} \{\{a\},\{b\}\} \{\{a\},\{b\},\{a,b\}\} F1 \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, F3 \{\{a\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\},\{b,c\}, F7 \{\{c\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{c\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{a\},\{b\}\} \{\{a\},\{b\},\{c\}\} F11 \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c\}\} \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c\}\} \{\{a\},\{c\}\} \{\{b\},\{c\}\} F14 \{\{a,c\},\{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} F17 \{\{b,c\},\{a,b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\},\{b,c\}, F18 \{\{a,b,c\}\} \{\{c\},\{a,b\},\{a,c\},\{b,c\}\} \{\{a\},\{b\},\{a,c\},\{b,c\}\} \{\{a\},\{b\},\{c\},\{a,c\},\{b,c\}, \{a,b,c\}\} -\{?\} \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c\}\} \{\{a\},\{c\},\{b,c\},\{a,b,c\}\} \{\{b\},\{c\},\{a,c\},\{a,b,c\}\} F18 \{\{a,b,c\}\} \{\{b\},\{a,b\},\{a,c\},\{b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\}\} \{\{a\},\{b\},\{c\},\{a,b\}, \{a,c\}, \{a,b,c\}\} -\{?\} \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c \}\} \{\{b\},\{c\},\{a,b\},\{a,b,c\}\} \{\{a\},\{b\},\{a,c\},\{a,b,c \}\} Filter chain \# 34 and its STRT spectrum b\}, \{a,c\}, \{b,c\},\{a,b,c\}\} Volume XX Issue I Version I F15 \{\{a,b\},\{a,b,c\}\} \{\{b\},\{c\},\{a,c\},\{b,c\}\} \{a,b,c\}\} \{\{a\},\{a,b,c\}\} \{\{b\},\{c\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{b\},\{a,b,c\}\} 67 F11 \{\{a,b\},\{a,c\},\{b,c\},\{a,b, c\}\} \{\{a,b\},\{a,c\},\{b,c\},\{a,b,c \}\} \{\{b\},\{c\}\} \{\{a\},\{b\}\} F12 \{\{a,b\},\{a,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{b,c\}\} \{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\},\{b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\}, Year 2020 F6 \{\{b\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{a,b,c\}\} \{\{a\},\{c\}\} \{\{a\},\{b\},\{c\}\} \{\{b\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{b\}\} F4 \{\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} ,c\}\} \{\{a\}\} \{\{b\},\{c\},\{a,b\},\{a,c\},\{b,c\},\{a,b \{b,c\},\{a,b,c\}\} Filter chain \# 33 and its STRT spectrum F1 \{\{a\},\{b\},\{c\},\{a,b\},\{a,c \}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{b,c\},\{a,b,c\}\} \{b,c\},\{a,b,c\}\} a,c\}, \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{\{a\},\{b\},\{c\},\{a,b\},\{ F1 \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\},}\\
F18\tabcellsep \{\{a,b,c\}\}\tabcellsep \{\{c\},\{a,b\},\{a,c\},\{b,c\}\}\tabcellsep c\}\} \{\{a\},\{b\},\{a,c\},\{b,c\}\}\tabcellsep \{\{b\}\} \{\{a\},\{b\},\{a,b\},\{a,c\},\{b ,c\},\end{longtable} \par
  {\small\itshape [Note: F1\{\{a\},\{b\},\{c\},\{a,b\},\{a,c  \},  \{b,c\},\{a,b,c\}\}   \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\},  \{b,c\},\{a,b,c\}\}   \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\},  \{b,c\},\{a,b,c\}\}   \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\},  \{b,c\},\{a,b,c\}\}    Global Journal of Computer Science and TechnologyVolume XX Issue I Version IF13 \{\{a,b\},\{b,c\},\{a,b,c\}\}  \{\{a\},\{b\},\{c\},\{a,c\}\}  \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\},  \{b,c\}\}   \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\},  \{b,c\},\{a,b,c\}\}   F15 \{\{a,b\},\{a,b,c\}\}  \{\{a\},\{c\},\{a,c\},\{b,c\}\}  \{\{a\},\{c\},\{a,b\},\{a,c\},\{b,F1   \{\{a\},\{b\},\{c\},\{a,b\},\{a,c  \},  \{b,c\},\{a,b,c\}\}   \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}  ,  \{b,c\},\{a,b,c\}\}   \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\},  \{b,c\},\{a,b,c\}\}   \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\},  \{b,c\},\{a,b,c\}\}   F3  \{\{a\},\{c\},\{a,b\},\{a,c\},  \{b,c\},\{a,b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,\{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} F17 \{\{b,c\},\{a,b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\}\} \{\{a\},\{c\},\{a,b\},\{a,c\},\{b,c\}, \{a,b,c\}\} \{\{b\},\{a,b,c\}\} F18 \{\{a,b,c\}\} \{\{a\},\{a,b\},\{a,c\},\{b,c\}\} \{\{b\},\{c\},\{a,c\},\{b,c\}\} \{\{a\},\{b\},\{c\},\{a.c\},\{b,F1 \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\}, \{b,c\},\{a,b,c\}\} F3 \{\{a\},\{c\},\{a,b\},\{a,c\},\{b,c\},\{a,b,c\}\}   \{\{a\},\{c\},\{a,b\},\{a,c\},  \{b,c\},\{a,b,c\}\}   \{\{a\},\{c\},\{a,b\},\{a,c\},\{b,c\},  \{a,b,c\}\}  \{\{b\}\}   ,\{a,c\},\{b,c\},\{a,b,c\}\} \{\{a\},\{c\},\{a,b\},\{a,b,c\}\}  \{\{b\},\{c\},\{b,c\},\{a,b,c\}\}    Filter chain \# 28 and its STRT spectrumF1\{\{a\},\{b\},\{c\},\{a,b\},\{a,c\},  \{b,c\},\{a,b,c\}\}   \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\},  \{b,c\},\{a,b,c\}\}   \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\},  \{b,c\},\{a,b,c\}\}   \{\{a\},\{b\},\{c\},\{a,b\},\{a,F13 \{\{a,b\},\{b,c\},\{a,b,c\}\}  \{\{a\},\{b\},\{c\},\{a,c\}\}  \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\},  \{b,c\}\}   \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\},  \{b,c\},\{a,b,c\}\}   F15 \{\{a,b\},\{a,b,c\}\}  \{\{b\},\{c\},\{a,c\},\{b,c\}\}  \{\{b\},\{c\},\{a,b\},\{a,c\},  \{b,c\},\{a,b,c\}\} \{\{a\},\{a,b,c\}\} F18 \{\{a,b,c\}\} \{\{b\},\{a,b\},\{a,c\},\{b,c\}\} \{\{a\},\{c\},\{a,b\},\{b,c\}\} \{\{a\},\{b\},\{c\},\{a,b\},\{b,c\},F1  \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\},  \{b,c\},\{a,b,c\}\}   \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\},  \{b,c\},\{a,b,c\}\}   \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\},  \{b,c\},\{a,b,c\}\}   \{\{a\},\{b\},\{c\},\{a,]} 
\caption{\label{tab_5}}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2} \par 
\begin{longtable}{P{0.34\textwidth}P{0.51\textwidth}}
Filter No.\tabcellsep Filter Elements\end{longtable} \par
 
\caption{\label{tab_9}Table 2 :}\end{figure}
 			\footnote{© 2020 Global Journals Set Theoretic Rajan Transform and its Properties} 		 		\backmatter   			 
\subsection[{Acknowledgement}]{Acknowledgement}\par
The first author thanks the second author Professor E. G.  			  			   {\ref F1 \{\{a\},\{b\},\{c\},\{d\},\{a,b\},\{a,c\},\{a,d\},\{b,c\},\{b,d\}, \{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} \{\{a\},\{b\},\{c\},\{d\},\{a,b\},\{a,c\},\{a,d\},\{b,c\},\{b,d\},\{c,d\}, \{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} F2 \{\{a\},\{b\},\{c\},\{a,b\},\{a,c\},\{a,d\},\{b,c\},\{b,d\},\{c,d\}, \{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} \{\{d\}\} F7 \{\{a\},\{c\},\{a,b\},\{a,c\},\{a,d\},\{b,c\},\{b,d\},\{c,d\}, \{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} \{\{b\},\{c\},\{d\}\} F13 \{\{a\},\{a,b\},\{a,c\},\{a,d\},\{b,c\},\{b,d\},\{c,d\},\{a,b,c\}, \{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} \{\{c\},\{d\}\} F22 \{\{a\},\{a,b\},\{a,c\},\{a,d\},\{b,c\},\{b,d\},\{a,b,c\}, \{a,b,d\}, \{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} \{\{b\},\{c\},\{d\},\{b,c\},\{b,d\},\{c,d\},\{b,c,d\}\} F36 \{\{a\},\{a,b\},\{a,c\},\{a,d\},\{b,c\},\{a,b,c\},\{a,b,d\}, \{a,c,d\}, \{b,c,d\},\{a,b,c}  {\ref \{a,b,c,d\}\} \{\{a\},\{b\},\{c\},\{d\},\{a,b\},\{a,c\},\{a,d\},\{b,c\},\{b,d\},\{c,d\}, \{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} F132 \{\{a,b\},\{a,c\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{a,b,c,d\}\} \{\{d\},\{a,b,c,d\}\} F145 \{\{a,b\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{a,b,c,d\}\} \{\{b\},\{c\},\{d\},\{a,b,c\},\{a,b,d\},\{a,b,c,d\}\} F155 \{\{a,b\},\{a,b,c\},\{a,b,d\},\{a,b,c,d\}\} \{\{c\},\{d\},\{a,b,c,d\}\} F161 \{\{a,b,c\},\{a,b,d\},\{a,b,c,d\}\} \{\{b\},\{c\},\{d\},\{a,b\},\{a,c\},\{a,d\},\{b,c\},\{b,d\},\{c,d\}, \{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} F265 \{\{a,b,c\},\{a,b,c,d\}\} \{\{d\},\{a,d\},\{b,c,d\},\{a,b,c,d\}\} F166 \{\{a,b,c,d\}\} \{\{b\},\{c\},\{d\},\{a,c\},\{a,d\},\{b,c\},\{b,d\},\{a,b,c\}, \{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} \{?\} \{\{c\},\{d\},\{a,d\},\{b,d\},\{a,b,d\},\{a,c,d\},\{b,c,d\}, \{a,b,c,d\}\}} 			 			  				\begin{bibitemlist}{1}
\bibitem[11 F29 {{c},{a,c},{a,d},{b,c},{b,d},{c,d},{a,b,c},{a,b,d},{a,c,d},{b,c,d},{a,b,c,d}} 11 F30 {{c},{a,b},{a,c},{b,c},{b,d},{c,d},{a,b,c},{a,b,d},{a,c,d},{b,c,d},{a,b,c,d}} 11 F31 {{c},{a,b},{a,c},{a,d},{b,c},{c,d},{a,b,c},{a,b,d},{a,c,d},{b,c,d},{a,b,c,d}} 11 F32 {{d},{a,c},{a,d},{b,c},{b,d},{c,d},{a,b,c},{a,b,d},{a,c,d},{b,c,d},{a,b,c,d}} 11 F33 {{d},{a,b},{a,d},{b,c},{b,d},{c,d},{a,b,c},{a,b,d},{a,c,d},{b,c,d},{a,b,c]{b0}\label{b0} 	 		\textit{11 F29 \{\{c\},\{a,c\},\{a,d\},\{b,c\},\{b,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 11 F30 \{\{c\},\{a,b\},\{a,c\},\{b,c\},\{b,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 11 F31 \{\{c\},\{a,b\},\{a,c\},\{a,d\},\{b,c\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 11 F32 \{\{d\},\{a,c\},\{a,d\},\{b,c\},\{b,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 11 F33 \{\{d\},\{a,b\},\{a,d\},\{b,c\},\{b,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c},  		b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\}.  	 	 (d\}\} 11 F25 \{\{b\},\{a,b\},\{a,d\},\{b,c\},\{b,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 11 F26 \{\{b\},\{a,b\},\{a,c\},\{b,c\},\{b,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 11 F27 \{\{a,b\},\{a,c\},\{a,d\},\{b,c\},\{b,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 11 F28 \{\{b\},\{a,b\},\{a,c\},\{a,d\},\{b,c\},\{b,d\},\{a. d\}\} 11 F34 \{\{d\},\{a,b\},\{a,c\},\{a,d\},\{b,d\},\{c,d\},\{a,b,c\},\{a,b,d\},\{a,c,d\},\{b,c,d\},\{a,b,c,d\}\} 11) 
\bibitem[Rajan ()]{b2}\label{b2} 	 		‘On the Notion of Generalized Rapid Transformation’.  		 			E Rajan 		.  	 	 		\textit{World multi conference on Systemics, Cybernetics and Informatics}  		July 7 -11, 1997.  	 
\bibitem[References Références Referencias]{b1}\label{b1} 	 		\textit{References Références Referencias},  		 	 
\end{bibitemlist}
 			 		 	 
\end{document}
