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E9 205 Machine Learning for Signal Processing
22-08-2016
Linear Predictive Analysis
Linear Prediction
❖ Current sample expressed as a linear
combination of past samples
n n-1 n-2 n-3
a3 a2 a1
E9 205 Machine Learning for Signal Processing Linear Predictive - - PowerPoint PPT Presentation
E9 205 Machine Learning for Signal Processing Linear Predictive - - PowerPoint PPT Presentation
E9 205 Machine Learning for Signal Processing Linear Predictive Analysis 22-08-2016 Linear Prediction Current sample expressed as a linear combination of past samples n- 3 n- 2 n- 1 n a 1 a 2 a 3 Properties of LP Error signal (for the
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Properties of LP
Error signal (for the optimal predictor) is orthogonal to the samples used in the predictor. Using the orthogonality property -> normal equations Autocorrelation matrix is Hermitian symmetric.
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Properties of LP
Forward linear prediction filter except for line spectral process Properties of
- stability (all roots )
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Properties of LP
AR(N) process - Any WSS process which satisfies Filter is stable - error signal is white Approximating by i.e. with
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Properties of LP
AR(N) process - Any WSS process which satisfies Filter is stable - error signal is white Approximating by i.e. with Autoregressive modeling
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Properties of LP
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Properties of LP
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Properties of LP
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Linear Prediction
AR Model of the Power Spectrum of the Signal
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Applications of Autoregressive Modeling
❖ Economics - Macroeconomic variabilities ❖ Statistics - System Identification. ❖ Geophysics - Oil Exploration. ❖ Neurophysics - EEG signal analysis (rhythms) ❖ Speech Communication - Coding, Recognition.
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Linear Prediction for Speech
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Source Filter Model of Speech
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Feature Extraction for Speech/Audio
Frequency Time Frequency
Conversion to Spectrogram
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Feature Extraction for Speech/Audio
Time Frequency
Integration to Mel-scale
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Feature Extraction for Speech/Audio
Integration to Mel-scale
Time Frequency
Mel
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Feature Extraction for Speech/Audio
Integration to Mel-scale
Time Frequency
Log + DCT
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Feature Extraction for Speech/Audio
Conversion to features - Mel frequency cepstral coefficients (MFCC)
Time Frequency
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Recap so far …
❖ Signal analysis - STFT ❖ Choice of suitable window, time frequency resolution. ❖ STFT factorization ❖ NMF - cost function, auxiliary function, divergence,
applications in speech/audio.
❖ Signal Analysis - linear prediction ❖ Orthogonality of error, normal equations,
approximation with AR(N) process, autoregressive modeling.
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