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\title{Time Stretching using Phase Vocoder}
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\begin{document}

             \author[1]{Vignesh  Ganesan}

             \affil[1]{  Jasmin Infotech Pvt Ltd}

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\date{\small \em Received: 14 December 2015 Accepted: 31 December 2015 Published: 15 January 2016}

\maketitle


\begin{abstract}
        


Introduction-Time Scale Modification (TSM) is a principle that is used to modify the time axis or time resolution. This concept can be used in Audio processing as well as Image processing. In this research work, TSM concept is used to perform Time Stretching of an audio signal. In this concept , the speed of the audio playback is changed without affecting audio signal's pitch. The time stretching concept has been used extensively in different application, such as in post production for effects, during music mixing. This is also used in the application to capture or play back a slow motion video. If we look at the current scenario, Time Stretching is extensively used in the field of entertainment, and creative arts.My paper talks about using this Time Stretching in the Automobile Industry. Now a days we have different types of FM stations (Digital and Analog). There is one particular scenario which I have considered as the Problem statement.

\end{abstract}


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\let\tabcellsep& 	 	 		 
\section[{I. Introduction}]{I. Introduction}\par
ime Scale Modification (TSM) is a principle that is used to modify the time axis or time resolution. This concept can be used in Audio processing as well as Image processing. In this research work, TSM concept is used to perform Time Stretching of an audio signal. In this concept , the speed of the audio playback is changed without affecting audio signal's pitch. The time stretching concept has been used extensively in different application, such as in post production for effects, during music mixing. This is also used in the application to capture or play back a slow motion video.\par
If we look at the current scenario, Time Stretching is extensively used in the field of entertainment, and creative arts. 
\section[{II. USE CASE SCENARIO : FM-DAB Linking}]{II. USE CASE SCENARIO : FM-DAB Linking}\par
In the concept of Seamless Linking, the FM (Frequency Modulation) would be playing ahead of DAB (Digital Audio Broadcasting). In this case, when switching is necessary from FM to DAB, we would need to wait for an amount 3 seconds (assuming that the delay between FM and DAB is 3 seconds). Assuming a delay of 3 seconds, In the above example, FM is playing the 5th second of an audio, at the same instant DAB would be playing the 2nd second of the same audio. Now at this point if we need to switch from FM to DAB, we would again hear, 2,3 and 4th second audio before hearing the 5th second audio, So 3 seconds of audio will repeat. In alternate case, if we do not want to hear the same audio again, there would be 3 seconds of audio mute and playback would resume from 5th second in DAB.\par
In seamless linking this is avoided and a concept called Time Stretching is introduced. In the same example, without switching it immediately, the FM signal from 6th second till 11th second (total duration 6seconds) is stretched to 9 seconds.\par
The following buffer diagram depicts different stages of stretching and its corresponding pointer location of the DAB signal.   
\section[{G}]{G}\par
My paper talks about using this Time Stretching in the Automobile Industry. Now a days we have different types of FM stations (Digital and Analog). There is one particular scenario which I have considered as the Problem statement.\par
Author: e-mails: vigneshganesh89@gmail.com, vignesh\textunderscore thyagarajan@srmuniv.edu.in    G channel etc. The algorithm has been designed in such a way to accommodate different number of channel. For every channel the same process would be applied. Being the 1st stage, it is responsible for converting the time domain signal to a frequency domain signal. The concept that has been applied here is Short Time Fourier Transform. In general cases a Fourier Transform would be sufficient to convert the time domain signal to a frequency domain signal. This would only result in a single conversion and we would not have much details about what frequency is present at what instant of time. 
\section[{III. Algorithm Overview}]{III. Algorithm Overview}\par
To get more precise details about which frequency is present at which time slot STFT is carried out. This is done taking FFT to the signal at different time slots. The output of this stage would be a Multi Dimensional array with each column representing frequency component at a particular time slot. 
\section[{Stage 2: Phase Vocoder}]{Stage 2: Phase Vocoder}\par
The output of the STFT stage will act as the input to this stage. This module performs the core of time stretching. Phase Vocoder stretches time in frequency domain. The input data to this stage is in complex form and is in frequency domain. Interpolation is the backbone concept of this Phase Vocoder. The algorithm estimates a phasor, which is used to modify the existing sample at a different time position. In this algorithm, I have used interpolation using two columns. The output of this stage will be in frequency domain, it would be a multi dimensional array (2D Matrix) having same number of rows as the input but number of columns would vary according to the stretching desired.\par
Stage 3: ISTFT This stage performs Inverse STFT. Input to this module is the output of the Phase Vocoder. Here IFFT has to be performed several times to get back the stretched time domain signal. The only major difference in applying the IFFT is that the output of every IFFT has to follow overlap addition process. This overlap method will avoid the phase discontinuity and amplitude reduction at the frame border. 
\section[{VI.}]{VI.} 
\section[{Simulation Results}]{Simulation Results}\par
Implementation of this algorithm has been successfully evaluated in MATLAB Platform. Both graphical evaluation and psychoacoustic listening tests were also conducted. Some of the simulation results are described below.\par
Figure  {\ref 3} : Audio Time Stretching (Frame by Frame): Input Frame vs Stretched Output Frame Fig.  {\ref 3}. represents the analysis of just one frame iteration. According to the above iteration, the input is of 2048 samples and from the output graph it is evident that it has been stretched close to 2450 samples. This output will not be the final data written to the file. There will be overlap addition taking place, so that the end segment will be compensated and there would be no data loss. This graphical representation is just for a basic understanding of how this algorithm works frame by frame. The next representation would show the overall input vs output audio signal with respect to the entire song duration of 6 seconds.  
\section[{VII. Conclusion and Future Scope}]{VII. Conclusion and Future Scope}\par
Though this algorithm was mainly created and developed to work for real time scenario, at present this algorithm has been successfully tested and verified under MATLAB platform. Once this algorithm is converted to Embedded C domain, then it would work in real time scenario. This algorithm needs to be linked to a seamless linking algorithm for maximum efficiency. To achieve that just certain parameters needs to be tweaked and nothing major needs to be done at the root level of the algorithm.\par
In general cases of Time Stretching, the audio is processed for the entire selection or a file, but in this concept it works on a frame by frame basis which is what makes it unique to work in a real time scenario such as an Automobile.\par
The phase discontinuity is suppressed almost to an unnoticeable change, and the phasiness effect has also been reduced. This algorithm has been designed for an optimal solution which is a good enough quality (the effect of time stretching is not too disturbing for the human ear), and a medium sized computational complexity.\begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-2.png}
\caption{\label{fig_1}FM}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{1}\includegraphics[]{image-3.png}
\caption{\label{fig_2}Figure 1 :}\end{figure}
     			\footnote{© 2016 Global Journals Inc. (US)} 			\footnote{© 2016 Global Journals Inc. (US) Time Stretching using Phase Vocoder} 		 		\backmatter  			  				\begin{bibitemlist}{1}

\end{bibitemlist}
 			 		 	 
\end{document}
