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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. enter image description here

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  • $\begingroup$ Hm, the wikipedia article on matched filter explicitly states the shape it needs to have? Also, you know what the result of matched filtering should be, so simply check for that. $\endgroup$ – Marcus Müller Jul 24 at 16:23
  • $\begingroup$ @MarcusMüller The Wikipedia matched filter article is very general. Using the article does not give insight into what the output of a matched filter looks like for LFM vs a Barker Code, for example. However I do agree that a bit of Googling would quickly yield what the OP is looking for. $\endgroup$ – Envidia Jul 24 at 16:54
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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

enter image description here

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.

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  • $\begingroup$ Thanks for the response.I am new to signal processing and learning how to interpret these graphs. $\endgroup$ – level2fast Jul 24 at 23:42
  • $\begingroup$ I like your answer. I've done what you suggested above and confirmed that the matched filter output without noise is what you expect. Assuming you are working with real world signals that have added noise how would you confirm that the new output with noise is correct without looking at a plot? I am trying to think of way that involved the use of some sort of data to prove this. The user above suggests that I can use the auto-correlation function to determine this. $\endgroup$ – level2fast Jul 25 at 0:08
  • $\begingroup$ @level2fast Dilip is right. What you are seeing is the output of the autocorrelation, which is what the matched filter produces. When noise is added, the matched filter still is used to attempt and extract the highest SNR possible. The output now might be distorted and may not look exactly like what I've shown. However you should get some type of SNR gain when doing this process. Test it yourself: add just a little noise and see what the result looks like. $\endgroup$ – Envidia Jul 25 at 4:47
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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.

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  • $\begingroup$ Thanks for the response. So if I wanted to confirm my matched filter output using some other method besides plotting the time domain signal I would need to know the expected auto-correlation signal ahead of time and then compare it to my output correct? The auto-correlation function for a linear fm chirp signal is a sinusoid with quadratic phase. $\endgroup$ – level2fast Jul 24 at 23:59
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    $\begingroup$ @level2fast The autocorrelation function of a linear FM chirp signal is not a sinusoid with quadratic phase; it is the linear FM chirp signal itself that is a sinusoid with quadratic phase. $\endgroup$ – Dilip Sarwate Jul 25 at 15:20

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