Just wonder what kind of spectrum analysis is used. FFT or sth else? If I understand correctly. MPC should do spectrum analysis first then apply psychoacoustic model and quantization in each sub-band. Is this right?

I don't think it uses FFT. The SV7 decoder certainly doesn't require an inverse transform, since it's a subband (time-domain) coder.

EDIT: I was not entirely correct. Read this.

FFT is used for analysis, but isn't coded in the output.

MPC uses FFT for psychoacoustic calculations. The actual coding doesn't use mdct transform unlike mp3,aac,vorbis etc.. But for creating of the masking threshold and other psychoacoustic analysis, frequency domain is used.

Is wavelet better for this job? I heard that wavelet have better time resolution at high frequency and better frequency resolution at lower frequency.

wavelets have better time-locality (or how this should be said in english?), that makes them potentionally better for transform codecs. but I have not heard about using them for psy models, and I'm not sure they will be really better. good psy model is mostly the result of numerous tunnings and tweakings

There is a tradeoff between time and frequency resolution and wavelets can balance it by using higher frequency resolution at low frequencies and higher time resolution at higher frequencies. But generally, wavelets isn't as easy to work with for audio than it is for video.