I have written a matched filter in matlab to compress a linear FM chirp signal and would like to confirm that the results of my range compression. My question is what is the best way to do this? I know that when looking at the plot of the output of the matched filter you should see something like the image below, but was wondering if there is a more scientific way to confirm that the output of the matched filter is correct.
If all you want to do is simply check that the output of the matched filter is correct, do it without noise. The autocorrelation should have a distinct shape that you can look up anywhere online. It is sinc-like and will have a general shape like this
The pulse width and the bandwidth of the chirp will change where the nulls are located and the width of the lobes, but the general shape will remain the same.
In the absence of noise, the output of the matched filter is exactly the autocorrelation function of the input signal, delayed in time so that the peak autocorrelation is at the chosen sampling time (cf. the first part of this answer on this forum). I don't recall off the top of my head what the autocorrelation function of a linear FM chirp signal is, but the sharp peak that in your bottom trace suggests that the autocorrelation function is sharply peaked, perhaps like a sinc function with very small null-to-null distance.