Analysis and Synthesis of Pseudo-Periodic 1/f-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 1/f components, that is, by a pseudo-periodic 1/f-like process. Due to the fundamental selfsimilar character of the wavelet transform, 1/f 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.

Keywords

• wavelets
• 1/f-noise
• spectral modeling.