# Stolt interpolation and ifft in range migration algorithm

I am using range migration algorithm for focusing stripmap synthetic aperture radar data. I have successfully tested my algorithm using the following steps after range compression (similar to this link)

1. 2D FFT the data,
2. Multiply data with exp(1i.*Krange*reference range)
3. Interpolate omega to Krange,
4. Inverse 2D FFT

However, when applying the above mentioned steps to the real SAR data, the algorithm works only till step 2 but returns totally blurred image with steps 3 and 4 accomplished. I am not sure if the problem is with the interpolator or ifft (as it is being applied on a non-uniform grid). My questions are:

1. How to choose the right interpolator for complex data? I have tried interpolating real and imaginary parts separately with no success.
2. Does the ifft2 function in MATLAB operate properly on non-uniform data?

I will really appreciate any relevant answer. Thanks.

• The FFT algorithm will not work on non-uniform data. Start with a synthetic phase history for a single point at the center of the scene and walk through each step one at a time. As for interpolating complex data, the only difference is that the arithmetic is complex. – AnonSubmitter85 Feb 3 '20 at 11:44
• Thanks. But the FFT works for the non-uniform data obtained through simulation. I wonder why is it not working for the real data. – Rifat Afroz Feb 4 '20 at 2:04
• The FFT most certainly does not work on non-uniformly spaced data. You'll get an answer, but that answer will not be the spectrum of the underlying signal. – AnonSubmitter85 Feb 4 '20 at 12:58