PSD - Spectrum analysis
I'm a little confused by this statement given the previous one indicates you've already taken the FFT.


  Finally, I take each of the blocks (computed by the STFT) and perform PSD.


Generally the following is used; Seperate into frames (overlap if desired) -> apply window -> fft -> transform and scale into dB (if desired).

The scaling for a power spectrum or power spectral density can be a bit tricky at first, but this paper goes into some great detail about how to set it up.