#### Summary of LP Spectral Envelopes

In summary, the spectral envelope of the th spectral frame, computed by linear prediction, is given by(11.13) |

where is computed from the solution of the Toeplitz normal equations, and is the estimated rms level of the prediction error in the th frame. The stable, all-pole filter

(11.14) |

can be driven by unit-variance white noise to produce a filtered-white-noise signal having spectral envelope . We may regard (no absolute value) as the frequency response of the filter in a

*source-filter decomposition*of the signal , where the source is white noise. It bears repeating that is zero mean when is monic and minimum phase (all zeros inside the unit circle). This means, for example, that can be simply estimated as the mean of the log spectral magnitude . For best results, the frequency axis ``seen'' by linear prediction should be

*warped*to an auditory frequency scale, as discussed in Appendix E [123]. This has the effect of increasing the accuracy of low-frequency peaks in the extracted spectral envelope, in accordance with the nonuniform frequency resolution of the inner ear.

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