The purpose of this presentation is to demonstrate the practical interest of an original improvement of the classic Fourier analysis. The n-th order short-time Fourier Transform (FTn) extends the classic short-time Fourier transform by also considering the first n signal derivatives. This technique greatly improves Fourier analysis precision not only in frequency and amplitude but also in time, thus minimizing the well-known problem of the trade-off of time versus frequency. The implementation of this analysis method leads to an enhanced phase vocoder particularly wellsuited for extracting spectral parameters from the sounds.