From Volatility Modeling of Financial Time-Series to Stochastic Modeling and Enhancement of Speech Signals

Modeling speech signals in the short-time Fourier transform (STFT) domain is a fundamental problem in designing speech enhancement systems. This chapter introduces a novel modeling approach, which is based on generalized autoregressive conditional heteroscedasticity (GARCH). GARCH is widely-used for volatility modeling of financial time-series such as exchange rates and stock returns. GARCH models take into account the heavy tailed distribution and volatility clustering characteristics of financial time-series. Spectral analysis shows that speech signals in the STFT domain are also characterized by heavy tailed distributions and volatility clustering. We demonstrate the application of GARCH modeling to speech enhancement, and show its advantage compared to using the conventional decision-directed method.

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