Analysis and Synthesis of Pseudo-Periodic-Like Noise by Means of Wavelets with Applications to Digital Audio

Abstract

Voiced musical sounds have nonzero energy in sidebands of the frequency partials. Our work is based on the assumption, often experimentally verified, that the energy distribution of the sidebands is shaped as powers of the inverse of the distance from the closest partial. The power spectrum of these pseudo-periodic processes is modeled by means of a superposition of modulated components, that is, by a pseudo-periodic-like process. Due to the fundamental selfsimilar character of the wavelet transform, processes can be fruitfully analyzed and synthesized by means of wavelets. We obtain a set of very loosely correlated coefficients at each scale level that can be well approximated by white noise in the synthesis process.

Our computational scheme is based on an orthogonal-band filter bank and a dyadic wavelet transform per channel. The channels are tuned to the left and right sidebands of the harmonics so that sidebands are mutually independent. The structure computes the expansion coefficients of a new orthogonal and complete set of harmonic-band wavelets. The main point of our scheme is that we need only two parameters per harmonic in order to model the stochastic fluctuations of sounds from a pure periodic behavior.