FFT along third dimension

Hi,

I am trying to understand the fft along 3rd dimension

a = [1 2 3 4; 5 6 7 8; 9 10 11 12];
b = [1 2 3 4; 5 6 7 8; 9 10 11 12];

num_samples = 3;
num_chirps = 4;
num_of_antenna = 2;
w_range = blackman(num_samples); 
w_doppler = blackman(num_chirps)'; 
w_angle = blackman(num_of_antenna); 
window_3d = w_range.*w_doppler.*permute(w_angle,[3 2 1]); 
window_2d = w_range .* w_doppler;


windowed_a = a.*window_2d;
windowed_b = b.*window_2d;
g1 = fft2(windowed_a);
g2 = fft2(windowed_b);
windowed_cat = cat(3,g1,g2).*permute(w_angle,[3 2 1]);
g3 = abs(fft(windowed_cat,[],3));

concat_3d = cat(3,a,b);
windowed_3d = concat_3d.*window_3d;
fft_2d = fft2(window_3d);
fft_3d = abs(fft(fft_2d,[],3));
ff_3d = abs(fftn(window_3d));

Shouldn't this be ture

g3==fft_3d==ff_3d

Why are they not equal?

Answer 1

[Matt J]

They are equal,

>> isequal(g3, fft_3d ), isequal(g3 , ff_3d )

ans =

  logical

   1


ans =

  logical

   1

although in general, I think you should expect they might differ by small floating point errors.

If you literally typed in g3==fft_3d==ff_3d, then this will not be true for the same reason the following is not:

>> 2==2==2

ans =

  logical

   0

[ARN]

somehow in MATLAB the answer is coming in 0's while in octave its giving me valid solution.

[Walter Roberson]

What release are you using, and which operating system? Also do you happen to have an AMD Jaguar CPU?

[ARN]

Release 2020, os : win 10 ,cpu intel

[Matt J]

And what is the magnitude of the differences between the arrays?

[ARN]

see the image

[Matt J]

Those look valid to me. Since w_angle contains only zeros, it makes sense that all fo the results should be approximately, if not exactly, zero.

>> w_angle = blackman(num_of_antenna)

w_angle =

     0
     0