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A Statistical and Spectral Model for Representing Noisy Sounds with Short-Time Sinusoids


We propose an original model for noise analysis, transformation, and synthesis: the CNSS model. Noisy sounds are represented with short-time sinusoids whose frequencies and phases are random variables. This spectral and statistical model represents information about the spectral density of frequencies. This perceptually relevant property is modeled by three mathematical parameters that define the distribution of the frequencies. This model also represents the spectral envelope. The mathematical parameters are defined and the analysis algorithms to extract these parameters from sounds are introduced. Then algorithms for generating sounds from the parameters of the model are presented. Applications of this model include tools for composers, psychoacoustic experiments, and pedagogy.

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Correspondence to Pierre Hanna.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Hanna, P., Desainte-Catherine, M. A Statistical and Spectral Model for Representing Noisy Sounds with Short-Time Sinusoids. EURASIP J. Adv. Signal Process. 2005, 182056 (2005).

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Keywords and phrases:

  • stochastic part of sounds
  • analysis and real-time synthesis of noisy sounds
  • spectral models
  • spectral density
  • musical transformations of sounds