Spectral Envelopes and Additive + Residual Analysis/Synthesis

Abstract

The subject of this chapter is the estimation, representation, modification, and use of spectral envelopes in the context of sinusoidal-additive-plus-residual analysis/synthesis. A spectral envelope is an amplitude-vs-frequency function, which may be obtained from the envelope of a short-time spectrum (Rodet et al., 1987; Schwarz, 1998). [Precise definitions of such an envelope and short-time spectrum (STS) are given in Section 2.] The additive-plus-residual analysis/synthesis method is based on a representation of signals in terms of a sum of time-varying sinusoids and of a non-sinusoidal residual signal [e.g., see Serra (1989), Laroche et al. (1993), McAulay and Quatieri (1995), and Ding and Qian (1997)]. Many musical sound signals may be described as a combination of a nearly periodic waveform and colored noise. The nearly periodic part of the signal can be viewed as a sum of sinusoidal components, called partials, with time-varying frequency and amplitude. Such sinusoidal components are easily observed on a spectral analysis display (Fig. 5.1) as obtained, for instance, from a discrete Fourier transform.