# Digital Signal Processing Module 8 Fast Convolution Using .

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Digital Signal ProcessingModule 8Fast Convolution using Overlap add and Save methodObjective:To understand and apply the overlap add and overlap save methods to find the response of LSIsystems.Introduction:Inspite of its computational advantages, there are some difficulties with the DFTapproach for finding linear convolution. For example, if x(n) is very long, we must commit asignificant amount of time computing very long DFTs and in the process accept very longprocessing delays. In some cases, it may even be possible that x(n) is too long to compute theDFT. The solution to these problems is to use block convolution, which involves segmentingthe signal to be filtered, x(n), into sections. Each section is then filtered with the FIR filterh(n), and the filtered sections are pieced together to form the sequence y(n). There are twoblock convolution techniques. The first is overlap-add, and the second is overlap-save.Description:Overlap Save Method:

Figure 8.1. Illustration of Overlap-save method of block convolution

Figure 8.2. Partitioning a sequence into subsequences of length M for the overlap-add method of blockconvolutionIllustrative Examples:Problem 1: Find the output y(n) of a filter whose impulse response is h(n) {1,1,1} and inputsignal x(n) {3,-1,0,1,3,2,0,1,2,1}usingi)Overlap - save methodii)Overlap - add methodSolution:

Summary:Therefore for long duration sequences the response of an LSI system can be found by usingblock convolution known as fast convolution using overlap - add and overlap - save methodsfaster than the methods using DFT and IDFT.Assignment:Problem 1: Find the output y(n) of a filter whose impulse response is h(n) {1,2} and inputsignal x(n) {1,2,-1,2,3,-2,-3,-1,1,1,2,-1}usingi)Overlap - save methodii)Overlap - add method

Simulation:%Overlap – Add methodclearclcx input('enter x:');h input('enter n---- ');ylabel('x(n)--- ');title('Input abel('n---- ');ylabel('h(n)--- ');title('Impulse response sequence');display('The fast convolution result using overlap-add method is:')y label('n---- ');ylabel('y(n)--- ');title('Fast Convolution using Overlap-Add method');Input:enter x:[3,-1,0,1,3,2,0,1,2,1]enter h:[1 1 1]Output:The fast convolution result using overlap-add method is:y 3220465334References:1. Digital Signal Processing, Principles, Algorithms and Applications – John G Proakis, Dimitris G Manolakis,Pearson Education / PHI, 20072. Discrete Time Signal Processing – A V Oppenheim and R W Schaffer, PHI, 20093. Digital Signal Processing – Monson H.Hayes – Schaum’s Outlines, McGraw-Hill,19994. Fundamentals of Digital Signal Processing using Matlab – Robert J Schilling, Sandra L Harris, Thomson2007.5. Digital Signal processing – A Practical Approach, Emmanuel C Ifeachor and Barrie W Jervis, 2 nd Edition, PE20096. Digital Signal Processing – A Computer Based Approach, Sanjit K.Mitra, McGraw Hill,2nd Edition, 2001

3. Digital Signal Processing – Monson H.Hayes – Schaum’s Outlines, McGraw-Hill,1999 4. Fundamentals of Digital Signal Processing using Matlab – Robert J Schilling, Sandra L Harris, Thomson 2007. 5. Digital Signal processing – A Practical Approach, Emmanue

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