High-precision Fourier analysis of sounds using signal derivatives

An original method is introduced which greatly improves the precision of the Fourier analysis not only in frequency and amplitude but also in time, thus minimizing the problem of the tradeoff of time versus frequency in the classic short-time Fourier transform. This method is of great interest when extracting spectral modeling parameters from existing sounds. A detailed theoretical presentation is made, and practical results obtained from implementing this method are presented.