Ifft2 results do not match that of irfft2 in Pyhton

Hi All,

I am using the rfft2 function in Python to get the Fourier trasnformed data and use the ifft2 function in Matlab to get back the original data.

I firstly, load the spectral data from Python

clear
clc 

rfft2_real = load('rfft2_real.txt');
rfft2_imag = load('rfft2_imag.txt');

Then I construct the whole spectral domain by adding the imaginary and real terms together

 
% Reconstruct the complex rfft2 output
rfft2_result = rfft2_real + 1i * rfft2_imag;

since rfft2 in Python stores only the positive frequencies for one of the dimensions I had to account for the missing negative frequencies in the follwoing way:

 
% Compute full FFT2 result by mirroring the data
[m, n_half] = size(rfft2_result);
n = 2 * (n_half - 1); % Reconstruct full FFT size
 
% Reconstruct the full frequency domain
fft2_result = zeros(m, n); 
fft2_result(:, 1:n_half) = rfft2_result; % Copy half-spectrum
fft2_result(:, n_half+1:n) = conj(fliplr(rfft2_result(:, 2:end-1))); % Mirror

% Compute the inverse FFT to get back the original matrix
reconstructed_x = ifft2(fft2_result)

I played with this code and it gives me the right answer for some signals but for others it does not. Anybody knows the issue?

[Matt J]

Please provide the input data files, both the cases that give the right answer and the ones that don't.

Answer 1

[Matt J]

I'm not a Python user, but if rfft2 only gives you positive x-frequencies, I would imagine it also only gives you positive y-frequencies as well, no? If so, why are you only mirroring across columns?