Estimation of chirp rates of music-adapted prolate spheroidal atoms using reassignment

摘要

We introduce a modified Matching Pursuit algorithm for estimating frequency and frequency slope of FM-modulatedmusic signals.The use of Matching Pursuit with constant frequency atoms provides coarse estimates which could beimproved with chirped atoms,more suited in principle to this kind of signals. Application of the reassignment method is suggested by its good localization properties for chirps. We start considering a family of atoms generated by modulation and scaling of a prolate spheroidal wavefunction~3.These functions are concentrated in frequency on intervals of a semitone centered at the frequencies of thewell-tempered scale. At each stage of the pursuit,we search the atom most correlated with the signal.We then consider the spectral peaks ateach frame of the spectrogram and calculate a modified frequency and frequency slope using the derivatives of thereassignment operators;this is then used to estimate the parameters of a cubic interpolation polynomial that models localpitch fluctuations.We apply the method both to synthetic and music signals.