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7/30/2019 Linear Predictive Coding-LPC
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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