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Analysis, Synthesis, and Perception of Musical Sounds pp 175–227Cite as

Spectral Envelopes and Additive + Residual Analysis/Synthesis

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Part of the book series: Modern Acoustics and Signal Processing ((MASP))

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.

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Authors
  1. XAVIER RODET
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  2. DIEMO SCHWARZ
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  1. Professor Emeritus School of Music Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, 61801, Urbana, IL, USA

    James W. Beauchamp

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RODET, X., SCHWARZ, D. (2007). Spectral Envelopes and Additive + Residual Analysis/Synthesis. In: Beauchamp, J.W. (eds) Analysis, Synthesis, and Perception of Musical Sounds. Modern Acoustics and Signal Processing. Springer, New York, NY. https://doi.org/10.1007/978-0-387-32576-7_5

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