Old style signal processing? I am wondering if "an array of overlapping band-pass ﬁlters" it is 'mostly' equivalent to a Short-Time Fourier transform. See this (figure down), where $s(t)$ is the signal;
LPF a second-order low-pass ﬁlter with a resonance frequency of 4 kHz; BPF an array of band-pass ﬁlters, where frequencies that are spaced equidistantly on
a critical band scale; HCM a hair cell model which is assumed identical in all channels, and finally a low-pass ﬁlter at 1250 Hz does an envelope extraction of the patterns in each channel. Processing a signal with this method produces a matrix of intesities that are vertically distributed like in STFT.

What are the differences between  them? Could be improved with wavelets as basis?

Thank you in advance. All comments will be rewarded!
there is a relationship between filterbank analysis and the STFT analysis, but it is not an identity.

perhaps it can be identical, where for filterbank, you are slicing the frequency domain into band slices and for STFT you are slicing the time domain into windowed segments (in audio we might call them "grains" or maybe sometimes "wavelets") in time.  but to make the two identical will require some thinking.  the BPF can't be simple regular-old BPFs.