FFT gives different answers according to what axis its applied to

I am seeing some behaviour with fft which I did not expect. It appears the output of the FFT depends on the axis to which it is applied.

In the following example - doing the FFT of the same data vector differs depending on whether you do fft, axis 1, data (100,1) compared to doing fft on axis 2 with the data shaped (1,100). I would expect these to be the same?

r = randn(100,1);
rf = fft(r);
rf1 = fft(r,[],1);
rt = r';
rtf = fft(rt,[],2);

sum(abs(rf-rf1))
sum(abs(rf-rtf'))

Even more worrying - ifft behaves the same way, so when reconstructing the original random array:

irf = ifft(rf);
irtf = ifft(rtf'); % this doesn't match irf
irtf2 = ifft(rtf,[],2); % this does match irf

Shouldn't irtf and irtf2 be the same? This seems quite dangerous to me - I thought it is standard to transpose data as required in Matlab and I would not expect to see differences in the output here.

Answer 1

[Guillaume]

The results are the same. Your problem is with the usage of ' aka ctranspose which computes the conjugate transpose of the input, i.e. not only transpose the vector but returns the conjugate of complex values.

To just do a plain transpose use the dotted version .' aka transpose:

r = randn(100, 1);
isequal(fft(r), fft(r, [], 1)) %return true
isequal(fft(r), fft(r.', [], 2).') %return true

edit: d'oh. Got my demo wrong!

Answer 2

[Thomas Koelen]

fft behaves the same in:

clc
close all
clear all
A=rand(1,100);
B=A';
X1=abs(fft(A));
X2=abs(fft(B));
figure(1)
plot(X1)
figure(2)
plot(X2)

Try this.