巨大的傅立叶矩阵-MATLAB [英] Huge Fourier matrix - MATLAB

问题描述

我需要创建一个傅立叶矩阵，以将其应用于需要使用spalloc定义为稀疏的巨大矩阵.我试过了:

I need to create a Fourier matrix in order to apply it to a huge matrix that I needed to define as sparse using spalloc. I tried:

F=dftmtx(N);

但是N太大，因此我无法创建它. 有什么办法可以解决这个问题? 谢谢您的帮助！

but N is too large so I can't create it. Is there any way to solve this problem? Thank you for your help!

推荐答案

对于每一列，您可以通过省略将乘以零的条目来形成简化的DFT矩阵.像

For each column, you can form a reduced DFT matrix by leaving out the entries that will multiply zeros. Something like

X = my_matrix;
c = column_index;

x = X(:,c);
N = length(x);
inds = find(x);
F = exp( -1j * 2*pi/N * (0:N-1)' * (inds-1) );
Xdft(:,c) = F * x(inds);

除非输入矩阵中的零不会更改列之间的列，否则您必须迭代列.但是，以上对我来说仍然很愚蠢.我只需一次拉出一列，然后使用fft().

You'll have to iterate over the columns unless the zeros in the input matrix don't change column-to-column. However, the above still seems silly to me. I'd just pull off one column at a time and use fft().

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