Linear Prediction Spectral Envelope

*Linear Prediction* (LP) implicitly computes a spectral envelope that
is well adapted for audio work, provided the order of the predictor is
appropriately chosen. Due to the error minimized by
LP, *spectral peaks* are emphasized in the envelope, as they are
in the auditory system. (The peak-emphasis of LP is quantified
in (10.10) below.)

The term ``linear prediction'' refers to the process of predicting a signal sample based on past samples:

We call the

Taking the *z* transform of (10.4) yields

(11.5) |

where . In signal modeling by linear prediction, we are given the signal but not the prediction coefficients . We must therefore

(11.6) |

where denotes the estimated prediction-error

(11.7) |

over some range of , typically an interval over which the signal is

If the prediction-error is successfully whitened, then the signal model can be expressed in the frequency domain as

(11.8) |

where denotes the power spectral density of (defined in Chapter 6), and denotes the variance of the (white-noise) prediction error . Thus, the

EnvelopeLPC | (11.9) |

- Linear Prediction is Peak Sensitive
- Linear Prediction Methods
- Computation of Linear Prediction Coefficients
- Linear Prediction Order Selection
- Summary of LP Spectral Envelopes

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University