Spectral Envelope Extraction

There are many definitions of spectral envelope. Piecewise-linear (or polynomial spline) spectral envelopes (applied to the spectral magnitude of an STFT frame), have been used successfully in sines+noise modeling of audio signals (introduced in §9.4). Here we will consider spectral envelopes defined by the following two methods for computing them:

1. cepstral windowing to lowpass-filter the log-magnitude spectrum (a ``nonparametric method'')

2. using linear prediction (a ``parametric method'') to capture spectral shape in the amplitude-response of an all-pole filter in a source-filter decomposition of the signal (where the source signal is defined to be spectrally flat)

In the following, denotes the th spectral frame of the STFT (§6.1), and denotes the spectral envelope of .

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Subsections

• Cepstral Windowing
• Linear Prediction Spectral Envelope
  • Linear Prediction is Peak Sensitive
  • Linear Prediction Methods
  • Computation of Linear Prediction Coefficients
  • Linear Prediction Order Selection
  • Summary of LP Spectral Envelopes
  
  
• Spectral Envelope Examples
  • Signal Synthesis
  • Spectral Envelope by the Cepstral Windowing Method
  • Spectral Envelope by Linear Prediction Method
  • Linear Prediction in Matlab and Octave

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Previous: Cross Synthesis
Next: Cepstral Windowing

Order a Hardcopy of Spectral Audio Signal Processing

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About the Author: 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.