# Matched Filter for Linear FM Waveform is not correct

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Alex Batts on 27 Apr 2022
Answered: Abhimenyu on 8 Dec 2023
I am attempting to implement the range-doppler algorithm for SAR processing. My range compression is great, but my azimuth compression is not working. When I attempt to create the azimuth matched filter (for a linear FM waveform), it comes out as a bunch of junk.
size_azimuth = 27975;
prf = 1679.9;
veff = 7121.2;
lambda = 0.0566;
R0 = 8.3090e5;
t = -size_azimuth/(2*prf):1/prf:size_azimuth/(2*prf)-1/prf; % Sets the time to sweep over
ka = 2*veff^2/(lambda*R0); % Sets azimuth chirp rate
pls_az = exp(1i*pi*ka*t.^2); % Definse azimuth chirp in time
When taking the fft of a chirp, it should look like a pulse. But, this comes out looking like a flat line, and I am not sure why.
Any help is greatly appreciated. (Full code can be provided, but I have just pulled out the relevant parts here).

Abhimenyu on 8 Dec 2023
Hi Alex,
I understand that you are encountering issues with the creation of the azimuth matched filter for a linear FM waveform in the context of Synthetic Aperture Radar (SAR) processing. Please refer to the below mentioned possible causes and solutions to the issue:
1. Chirp rate: A possible cause of the issue is that the azimuth chirp rate ka is too large, which makes the azimuth chirp too fast and the frequency spectrum too narrow. This can result in a flat line after taking the FFT. A possible solution is to reduce the value of ka by using a smaller effective velocity veff or a larger slant range R0” You can also try to increase the size of the azimuth window “size_azimuth” to improve the resolution.
2. Misalignment of chirp rate and Doppler centroid: The issue can also occur if the azimuth chirp is not aligned with the Doppler centroid of the raw data. This can result in a mismatch between the chirp and the data, which degrades the focusing quality. A possible solution is to estimate the Doppler centroid of the raw data and apply phase correction to the azimuth before taking the “FFT”.
3. Inappropriate modulation: A third possible cause is that the azimuth chirp is not modulated with the appropriate phase to distinguish the Doppler of the received signal. This can result in a loss of information and a poor image quality. A possible solution is to use the APC waveforms, which are modulated with a set of phases that make the Doppler of the received signal distinguishable.
I hope this helps to resolve the query.
Thanks,
Abhimenyu

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