Analysis and Regularization of Inharmonic Sounds via Pitch-Synchronous Frequency Warped Wavelets
Gianpaolo Evangelista, Sergio Cavaliere · University of Michigan Library Repository · 1997
We present several applications to sound analysis and synthesis of a novel time-frequency representation based on frequency warped wavelets, recently introduced by the authors.These wavelets are obtained from ordinary wavelets via Laguerre expansion.The discrete Laguerre transform is shown to be equivalent to a warping operation on the frequency axis.The amount of warping is controlled by the Laguerre parameter, which can be adapted to the characteristics of the signal.The concept is here applied to the Pitch-Synchronous Wavelet Transform (PSWT), also introduced by one of the authors.In our experiments we found that the inharmonicity characteristics of the piano are well approximated by our warping map family.The suitable Laguerre parameter may be found by means of optimazation techniques.Using the PS-FWWT we were able to achieve a good quality separation of the hammer noise in piano tones.This separation can be useful in sound synthesis both for employing the noisy components as excitation signals or for synthesizing the regular and noisy parts using different techniques.