Signal processing Compressed sensing : short-time Fourier transform matrix form.

Hello, Thank you for reading.

Recently, I am concerned in representing a chirp signal sum( sin(at^2+bt+c) ) in a sparse way. Thus, I need a sparse domain. It is said that STFT could be chosen.

Question 1, How could we find a sparse domain for a special signal? (As all we know sin(at+b) is sparse in DFT domain). Do we have another chose for chirp signal. And how to get their matrix form?

I start to construct the STFT matrix by myself.

For example, a signal with 64 samplings. I need a non-overlap, 4 parts STFT. Then, I cut the signal into 4 parts, and for each part I apply a hamming window then multiple by a 16 points DFT matrix. And repeat 4 time in column direction. Thus, I get a 16*64 STFT matrix.

Question 2: what I have done is right? Why a STFT is not a square matrix?

Looking forward to your reply!