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Overlap Save Method

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Performs convolution using the Overlap Save Method.

Overlap_Save_Method.m
% Theory
% 
% Overlap Save Method
% 
% In this method, the size of the input data blocks is N=L+M-1 and the DFTs and the IDFTs are of length L. Each Data Block consists of the 
% last M-1 data points of the previous block followed by L new data points to form a data sequence of length N=L+M-1.An N point DFT  is computed 
% for each data block. The impulse response of the FIR filter is increased in length by appending L-1 zeros and an N-point DFT of the sequence is 
% computed once and stored. The multiplication of the N-point DFTs for the mth block of data yields 
%                                                                    Ym(k)=h(k)Xm(k). 
% Since the data record is of length N, the first M-1 points of Ym(n)are corrupted by aliasing and must be discarded. The last L points of Ym(n) 
% are exactly the same as the result  from linear convolution. To avoid loss of data due to aliasing, the last M-1  points of each data record are
% saved and these points become the first M-1 data points of the subsequent record. To begin the processing, the first M-1 point of the first record
% is set to zero. The resulting data sequence from the IDFT are given where the first M-1 points are discarded due to aliasing and the remaining L 
% points constitute the desired result from the linear convolution. This segmentation of the input data and the fitting of the output data blocks together 
% form the output sequence. 
%
%
clc;
clear all;
x=input('Enter 1st sequence X(n)= ');
h=input('Enter 2nd sequence H(n)= ');
L=input('Enter length of each block L = ');

% Code to plot X(n)
subplot (2,2,1);
stem(x);
stem(x,'blue');
xlabel ('n---->');
ylabel ('Amplitude ---->');
title('X(n)');

%Code to plot H(n)
subplot (2,2,2);
stem(h);
stem(h,'black');
xlabel ('n---->');
ylabel ('Amplitude ---->');
title(' H(n)');

% Code to perform Convolution using Overlap Save Method
M=length(h);
lx=length(x);
r=rem(lx,L);
x1=[x zeros(1,L-r)];
nr=(length(x1))/L;
h1=[h zeros(1,L-1)];
for k=1:nr
    Ma(k,:)=x1(((k-1)*L+1):k*L)
    if k==1
        Ma1(k,:)=[zeros(1,M-1) Ma(k,:)];
    else 
        Ma1(k,:)=[Ma(k-1,(L-M+2):L) Ma(k,:)];        
    end
     Ma2(k,:)=ifft(fft(Ma1(k,:)).*fft(h1));
end
Ma3=Ma2(:,M:(L+M-1));
y1=Ma3';
y=y1(:)'

% Representation of the Convoled Signal
subplot (2,2,3:4);
stem(y,'red');
xlabel ('n---->');
ylabel ('Amplitude ---->');
title ('Convolved Signal');

% Add title to the Overall Plot
ha = axes ('Position',[0 0 1 1],'Xlim',[0 1],'Ylim',[0 1],'Box','off','Visible','off','Units','normalized', 'clipping' , 'off');
text (0.5, 1,'\bf Convolution using Overlap Save Method ','HorizontalAlignment','center','VerticalAlignment', 'top')

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