Auto correlation properties of window functions in pulse compression application

It is known that different window functions perform differently and users pick a window function (in amplitude modulation) based on their application or requirement.

I am trying to pick a window that has a good auto correlation response to be used in pulse compression (matched filtering) of ultrasonic transmit/receive waveforms. I am looking for a fair compromise between mainlobe width and mainlobe to side lobe dB fall. This can help identifying/detecting signals buried in coherent noise.

What is the best way to perform this analysis?

I have two approaches in mind,

1. Auto correlation of windowed linear chirps and calculating mainlobe width and mainlobe to side lobe dB fall

2. Calculating mainlobe width and mainlobe to side lobe dB fall of the frequency spectrum of autocorrelation of the window functions themselves.

Please let me know if any other analysis could be done to quantify this compromise and finding the best window function for my application.

• You're mixing up some different concepts here. Window functions are most often used for spectral analysis, and their mainlobe width and sidelobe rolloff characteristics control the tradeoff between frequency resolution and dynamic range. Good autocorrelation properties (ideally, an impulse function) are desired for waveforms used for pulse compression or spread-spectrum applications. It sounds like you're concerned about the latter, not about the spectral properties of the waveform. In that case, a linear FM chirp is a common choice for pulse-compression radar applications. Aug 23, 2017 at 14:19
• Imagine if I want to send a waveform and perform pulse compression afterwards (e.g. ultrasonic detection). I avoid sending FM chirp with a rectangular window. So I need to pick a window to modulate the FM chirp, e. g., Hann windowed FM chirp. Now, what are the criteria to choose Hann? How you go about with analysing window functions (e.g. Hann, Hamming, Kaiser, etc.) to perform the best in pulse compression. I have suggested 2 approaches in my question above. Which one do you think suits the most? Or are there any other analysis or consideration I could possibly take into account? Aug 23, 2017 at 14:41
• What is your goal when applying the window? Aug 23, 2017 at 17:37
• To perform pulse compression. I am avoiding rectangular FM chirp (~no window) due having high level of side lobes and giving rise to coherent noise in ultrasonic detection. So, I would window the FM chirp to minimise the effect of side lobes and achieve better spatial resolution. Aug 24, 2017 at 8:04
• you're definitely not getting a better resolution from windowing. Aug 25, 2017 at 19:11