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    Linear Predictive

    CodingTecniche avanzate per il Trattamento dei

    Segnali Audio

    Augusto Sarti

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    Idea and motivations

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    Idea and motivations

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    Data model

    z If we assume that the signal is modeled by alinear combination of past samples and asource signal we may write that

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    Data model

    z By Z-transforming the previous equation weobtain

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    Data model

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    Fundamentals of LPC

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    Fundamentals of LPC

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    Goal of prediction

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    Goal of prediction

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    Goal of prediction

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    Goal of linear prediction

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    Orthogonality principle

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    Wiener-Hopf equations

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    Wiener-Hopf equations

    z The above equations are known as Wiener-Hopf equations

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    Wiener-Hopf equations

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    Infinite memory Linear Prediction

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    Infinite memory Linear Prediction

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    Infinite Memory Linear Prediction

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    Infinite Memory Linear Prediction

    z Whitening process

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    Infinite Memory Linear Prediction

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    Computation of LPC parameters

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    Autocorrelation method

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    Covariance method

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    Frequency domain interpretation of LPC

    z Applying the DTFT to the error signal equationwe obtain that

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    Power Spectrum Envelope Matching

    z After some passages (and the use ofParsevals theorem) we obtain that the errorEn is

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    Power Spectrum Envelope Matching

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    Power Spectrum Envelope Matching

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    Power Spectrum Envelope Matching

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    Power Spectrum Envelope Matching

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    Power Spectral Envelope Matching

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    Power Spectral Envelope Matching

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    Power Spectral Envelope Matching

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    Frequency Selective LPC

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    Frequency Selective LPC

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    Frequency selective LPC

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    Applications of LPC

    z Speech coding/synthesisz Pitch Prediction (used in Codebook Excited

    Linear Prediction)z Computer Music: cross-synthesis

    z Spectral Envelope Estimation

    z ...

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    References

    z J.O.Smith, Lecture notes of MUS 240/ EE625, available athttp://ccrma.stanford.edu/~jos/pubs.html

    http://ccrma.stanford.edu/~jos/pubs.htmlhttp://ccrma.stanford.edu/~jos/pubs.html

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