I was wondering if it is possible to use windows of varying lengths when making a spectrogram based on the short-time Fourier transform (STFT). That is, for higher frequencies I would use shorter windows so that I get higher temporal resolution at the cost of poor spectral resolution. I understand this method will result in tradeoffs between time and frequency resolution just like in the continuous wavelet transform, as well as higher computational complexity.
I wanted to ask if there are any other disadvantages other than the ones mentioned above when the STFT is employed in such way since I could not find any literatures about it.
Thank you very much.