FFT on dim > 1 returning negative values?

I have a matrix that's [NxT] and I want the fft over the second dimension. But if I do this:

    X = rand(100,200);
    F1 = fft(X,[],2);
    F2 = fft(X')';

    figure;
    subplot(2,1,1);
    plot(real(F2)-real(F1));
    subplot(2,1,2);
    plot(imag(F2)-imag(F1));

Then, you can see, imag(F1) = -imag(F2). That is, F1 = conj(F2)

Is this a bug or am I misunderstanding something?

Answer 1

[Sean de Wolski]

This is caused because you are taking the complex conjugate transpose ('). If you take the regular transpose (.') you will see the behavior you are expecting:

X = rand(100,200);
F1 = fft(X,[],2);
F2 = fft(X.').'; %note the .'   
figure;
subplot(2,1,1);
plot(real(F2)-real(F1));
subplot(2,1,2);
plot(imag(F2)-imag(F1));

And for more info:

doc ctranspose %complex conjugate transpose
doc transpose %regular one

Answer 2

[Keith]

Whooooooooooooooooooooooooa. I did NOT know that! I've been using it for years. You seriously just blew my mind.

Now I get to go spend the next year going through all of my code.

Thanks so much for setting me straight!