Spectral Envelope Extraction

Let denote the spectrum of the th frame of the modulating signal . We desire to be the upper spectral envelope of . There are several definitions of spectral envelope:

• Cepstral smoothing
• Linear Prediction
• Piecewise linear peak connection or splines

Here we will consider only the first two. The third, piecewise-linear spectral envelopes, are often used in sines+noise modeling of audio signals (introduced in Chapter 7).

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Subsections

• Cepstral Smoothing
• Linear Prediction Spectral Envelope
  • Linear Prediction is Peak Sensitive
  • Computation of Linear Prediction Coefficients
  • Spectral Envelope
  • LPC Envelope Example: Speech vowel ``ah''
  • LPC Functions in Matlab and Octave

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Order a Hardcopy of Spectral Audio Signal Processing

Previous: Cross Synthesis
Next: Cepstral Smoothing

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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.