Cepstral Smoothing

The spectral envelope obtained by cepstral smoothing is defined as

where is a lowpass window in the cepstral domain, e.g.,

• The log-spectrum of is thus lowpass filtered (the complex cepstrum of is ``liftered'') to obtain a smooth spectral envelope.
• For voice, should be set below the pitch period in samples.
• Cepstral coefficients are typically used in speech recognition.
• For best results, use an audio-warped spectral axis, such as the ERB scale (Appendix E) or its early ancestor, the Mel frequency scale. Mel Frequency Cepstral Coefficients (MFCC) remain standard in speech recognition front ends.

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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.