DAFX: Digital Audio Effects, Second Edition

8.1 Introduction

Time—frequency representations give the evolution over time of a spectrum calculated from temporal frames. The notion of the spectral envelope extracted from such representations mostly comes from the voice production and recognition system: the voice production uses vocal chords as an excitation and the mouth and nose as a resonator system or anti-resonator. Voiced signals (vowels) produce a harmonic spectrum on which a spectral envelope is superimposed. This fact about voice strongly influences our way of recognizing other sounds, whether because of the ear or the brain; we are looking for such a spectral envelope as a cue to the identification or classification of sounds. This excitation-resonance model is also called source-filter model in the literature. Thus we can understand why the vocoding effect, which is the cross-synthesis of a musical instrument with voice, is so attractive for the ear and so resistant to approximations. We will make use of a source-filter model for an audio signal and modify this model in order to achieve different digital audio effects.

However, the signal-processing problem of extracting a spectral envelope from a spectrum is generally badly conditioned. If the sound is purely harmonic we could say that the spectral envelope is the curve that passes through the points related to these harmonics. This leaves two open questions: how to retrieve these exact values of these harmonics, and what kind of interpolation scheme should we ...