I've been studying the time-frequency uncertainty principle of Dennis Gabor, and the tradeoff of the STFT window size in representing the tonal and transient characteristics of the musical signal being studied.
I understand that by observing the spectrogram, one can see "blurry" temporal events (vertical lines) with a long window, and sharp frequency lines. The opposite is true, with blurry frequencies with a short window, and sharp temporal events.
Is there an objective measurement that can output a numerical value for "sharp vs. blurry" spectrogram visual comparison? Such that we can definitively say "for this signal x[n], the best STFT uses a window size of XYZ, which is the sparsest/least blurry/best representation". Is the term for this "sparsity"?