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