Lecture11 - Lecture 11 EE214A Abeer Alwan Linear Prediction...

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1 Lecture 11 EE214A Abeer Alwan Linear Prediction Coding (LPC)
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2 Historical Overview Analysis of the outputs of dynamical systems has lead to “time -series: analysis especially in Statistics Economics Communication systems Used in system identification and modeling First used in 1927 for ‘sunspot’ analysis Linear Prediction Concept Assume I/O relationship is h(n) s(n) u(n) q l l p k k l n u b G k n s a n s 0 1 ) ( ) ( ) ( Present output predicted from past values linearly “Linear prediction” Linear prediction coding (LPC) exploits redundancy in the signal to achieve lower bit rates
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3 Types of linear prediction LPC assumes an all-pole system AR (auto- regressive) all-zeros MA (moving average) poles & zeros ARMA p k k k q l l l z a b z G z U z S z H 1 0 1 ) ( ) ( ) ( The z-transform of the transfer function of the linear predictor is Common LP applications Neuro Physics Electrodes on patients scalp measure brain activity (EEG). Resonances indicate status of brain function/activity. Need to predict resonances. Geophysics Explode a dynamite, record vibration as seismic traces, use to determine structure of rock layers and/or presence of oil in an area. Speech Models speech spectra. All-pole (AR) model is used. Good method to predict resonances in vowels.
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4 Example of speech LPC spectrum AR all-pole model LPC: Speech Application Assume the speech signal is: The vocal-tract transfer function then is: Goal: Estimate a k ’s Note that A(z) is referred to as the inverse filter or prediction error filter ) ( ) ( ) ( 1 n u G k n s a n s p k k ) ( ) ( 1 ) ( ) ( 1 z H z A G z a G z U z S p k k k
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5 Speech Application Assume prediction signal is
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