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186 Chapter 5 THE DISCRETE FOURIER TRANSFORM
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function [y] = ovrlpsav(x,h,N)
% Overlap-Save method of block convolution
% ----------------------------------------
% [y] = ovrlpsav(x,h,N)
% y = output sequence
% x = input sequence
% h = impulse response
% N = block length
%
Lenx = length(x); M = length(h); M1 = M-1; L = N-M1;
h = [h zeros(1,N-M)];
%
x = [zeros(1,M1), x, zeros(1,N-1)]; % preappend (M-1) zeros
K = floor((Lenx+M1-1)/(L)); % # of blocks
Y = zeros(K+1,N);
% convolution with succesive blocks
for k=0:K
xk = x(k*L+1:k*L+N);
Y(k+1,:) = circonvt(xk,h,N);
end
Y = Y(:,M:N)’;
% discard the first (M-1) samples
y = (Y(:))’;
% assemble output
Note: The ovrlpsav function as developed here is not the most efficient
approach. We will come back to this issue when we discuss the fast Fourier
transform.
□ EXAMPLE 5.19 To verify the operation of the ovrlpsav function, let us consider the sequences
given in Example 5.18.
Solution
MATLAB script:
>> n = 0:9; x = n+1; h = [1,0,-1]; N = 6; y = ovrlpsav(x,h,N)
y =
1 2 2 2 2 2 2 2 2 2 -9 -10
This is the correct linear convolution as expected.
□
There is an alternate method called an overlap-add method of block
convolutions. In this method the input sequence x(n) ispartitioned into
nonoverlapping blocks and convolved with the impulse response. The resulting
output blocks are overlapped with the subsequent sections and
added to form the overall output. This is explored in Problem P5.32.
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