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Acyclic FFT Convolution in Matlab

The following example illustrates the implementation of acyclic convolution using a Cooley-Tukey FFT in matlab:

x = [1 2 3 4];
h = [1 1 1];

nx = length(x);
nh = length(h);
nfft = 2^nextpow2(nx+nh-1)
xzp = [x, zeros(1,nfft-nx)];
hzp = [h, zeros(1,nfft-nh)];
X = fft(xzp);
H = fft(hzp);

Y = H .* X;
format bank;
y = real(ifft(Y)) % zero-padded result
yt = y(1:nx+nh-1) % trim and print
yc = conv(x,h)    % for comparison
Program output:

nfft = 8
y =
  1.00  3.00  6.00  9.00  7.00  4.00  0.00  0.00
yt =
  1.00  3.00  6.00  9.00  7.00  4.00
yc =
     1     3     6     9     7     4


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``Spectral Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2011, ISBN 978-0-9745607-3-1.
Copyright © 2016-07-18 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA