Fourier-based methods for the spectral analysis of musical sounds

When dealing with musical sounds, the short-time Fourier transform prevails and sinusoids play a key role, according to both acoustics (vibrating modes) and psychoacoustics (pure tones). The values obtained when decomposing the signal on the time-frequency atoms are usually assigned to their geometrical center, leading to estimation errors for the sinusoidal parameters. To correct this, one can exploit the amplitude or phase information, use the derivatives of the analysis window, or those of the audio signal. This leads to three methods (phase vocoder, spectral reassignment, derivative algorithm) equally efficient: they are in fact different formulations of the best analysis method based on the Fourier spectrum.