Convolution in frequency domain (NOT CONVOLUTION IN TIME DOMAIN)
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chen xy
on 20 Jan 2013
Commented: bazrafshan88@gmail.com
on 29 Nov 2016
I know there are two theorem:
- convolution in time domain equals multiplication in frequency domain;
- multiplication in time domain equals convolution in frequency domain;
I am confused with the implementation with the 2nd in MATLAB. Here is my codes:
a = 1:5;
b = a+3;
A = fft(a);
B = fft(b);
c = a .* b
ans =
4 10 18 28 40
D = conv(A, B);
d = real(ifft(D))
d =
Columns 1 through 5
11.111 50.544 26.081 58.919 39.694
Columns 6 through 9
73.642 52.666 95.071 42.27
so my quesition is why the "a.*b" is not the same with "real(ifft(D))", is somewhere wrong? I know in the 1st theorem, the Nfft should be length(A)+length(B)-1, however, it seems not work here.
Any help will be thanks!
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Accepted Answer
Matt J
on 20 Jan 2013
Cyclic convolution is the dual of multiplication when dealing with discrete fourier transforms. You are doing linear convolution.
4 Comments
bazrafshan88@gmail.com
on 29 Nov 2016
Hi guys
How can I do the same for two matrices of the same size? say:
x = [3 5 4; 7 6 1; -1 2 0];
y = [2 7 1; 2 -3 2; 5 6 9];
how can I get the same results as x.*y using convolution of the fft2 of these two matrices?
Thanks in advance
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