Matlab fft2 (2D) giving interchanged values compared to multiple fft (1D) performed across rows and columns

Question

function [output1, output2] = fft2D(input)

   output1 = input';
   output1 = fft(output1);
   output1 = output1';
   output1 = fft(output1);

   output2 = fft2(input);
end

So I calculate in output2 the 2D FFT of input and in output1 the same 2D FFT of input. fft() applies, for a 2D matrix, FFT across the column vectors. So above I apply it over the rows and then over the columns.

However for a random matrix

 [1   1   4   1; 
  12  13  124 1;
  12  2   2   1;
  1   1   1   0]

my output1 is:

   1.0e+02 *

   1.7700 + 0.0000i  -1.0500 + 0.1400i   1.3700 + 0.0000i  -1.0500 - 0.1400i
  -0.1000 - 1.4700i  -0.0200 + 1.1100i  -0.0800 - 1.2100i  -0.2400 + 1.1300i
  -1.2900 + 0.0000i   1.1900 - 0.1200i  -1.0900 + 0.0000i   1.1900 + 0.1200i
  -0.1000 + 1.4700i  -0.2400 - 1.1300i  -0.0800 + 1.2100i  -0.0200 - 1.1100i

and my output2 is

   1.0e+02 *

   1.7700 + 0.0000i  -1.0500 - 0.1400i   1.3700 + 0.0000i  -1.0500 + 0.1400i
  -0.1000 - 1.4700i  -0.2400 + 1.1300i  -0.0800 - 1.2100i  -0.0200 + 1.1100i
  -1.2900 + 0.0000i   1.1900 + 0.1200i  -1.0900 + 0.0000i   1.1900 - 0.1200i
  -0.1000 + 1.4700i  -0.0200 - 1.1100i  -0.0800 + 1.2100i  -0.2400 - 1.1300i

They are the same values but interchanged in various positions! This has been driving me crazy for a long time, because from what I've (re)read online 2D FFT can be performed by applying 1D FFT across rows and then columns. Any help or suggestion would be great!

@AnderBiguri be more specific :P. The complex transpose is being used, not the real transpose. — rayryeng, Mar 01 '18 at 23:01

score 5 · Accepted Answer · answered Mar 01 '18 at 19:52

5

Use output1 = output1.' instead of output1 = output1' since the latter gives the conjugate transpose and you want the transpose.

function [output1, output2] = fft2D(input)
   output1 = input.';
   output1 = fft(output1);
   output1 = output1.';
   output1 = fft(output1);

   output2 = fft2(input);
end

Alternatively you can specify the dimension to take the FFT along.

function [output1, output2] = fft2D(input)
   output1 = fft(input,[],1);
   output1 = fft(output1,[],2);

   output2 = fft2(input);
end

answered Mar 01 '18 at 19:52

jodag

19,885
5
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1

I've been wracking my head for some time over where I've been going wrong, thank you for this! I've been thinking `'` was transpose till now... Thanks again! – four_lines Mar 01 '18 at 20:11
1

It's a mistake that many people have made (including myself). – jodag Mar 01 '18 at 20:16
2

@LuisMendo - This is for you. – rayryeng Mar 01 '18 at 20:33
3

@rayryeng One more for the [list](https://stackoverflow.com/a/25150319/2586922)! .-) – Luis Mendo Mar 01 '18 at 22:49
2

@LuisMendo Haha, that makes me feel better :P – four_lines Mar 02 '18 at 13:25

Matlab fft2 (2D) giving interchanged values compared to multiple fft (1D) performed across rows and columns

1 Answers1