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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 §10.4). 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, $ X_m(\omega_k)$ denotes the $ m$ th spectral frame of the STFT (§7.1), and $ Y_m(\omega_k)$ denotes the spectral envelope of $ X_m(\omega_k)$ .

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``Spectral Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2011, ISBN 978-0-9745607-3-1.
Copyright © 2022-02-28 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University