Convolution in frequency domain (NOT CONVOLUTION IN TIME DOMAIN)

23 次查看（过去 30 天）
chen xy
chen xy 2013-1-20
评论： bazrafshan88@gmail.com 2016-11-29
I know there are two theorem:
  1. convolution in time domain equals multiplication in frequency domain;
  2. 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!

请先登录，再回答此问题。

采纳的回答

Matt J
Matt J 2013-1-20
Cyclic convolution is the dual of multiplication when dealing with discrete fourier transforms. You are doing linear convolution.
  4 个评论
显示 2更早的评论
bazrafshan88@gmail.com
bazrafshan88@gmail.com 2016-11-29
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

请先登录，再进行评论。

更多回答（0 个）

类别

在 Help Center 和 File Exchange 中查找有关 Correlation and Convolution 的更多信息

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by