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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

  1. E9 205 Machine Learning for Signal Processing Linear Predictive Analysis 22-08-2016

  2. 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

  3. 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.

  4. Properties of LP Forward linear prediction filter Properties of - stability (all roots ) except for line spectral process

  5. Properties of LP AR(N) process - Any WSS process which satisfies Filter is stable - error signal is white Approximating by i.e. with

  6. 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

  7. Properties of LP

  8. Properties of LP

  9. Properties of LP

  10. Linear Prediction AR Model of the Power Spectrum of the Signal

  11. Applications of Autoregressive Modeling ❖ Economics - Macroeconomic variabilities ❖ Statistics - System Identification. ❖ Geophysics - Oil Exploration. ❖ Neurophysics - EEG signal analysis (rhythms) ❖ Speech Communication - Coding, Recognition.

  12. Linear Prediction for Speech

  13. Source Filter Model of Speech

  14. Feature Extraction for Speech/Audio Conversion to Spectrogram Frequency Frequency Time

  15. Feature Extraction for Speech/Audio Integration to Mel-scale Frequency Time

  16. Feature Extraction for Speech/Audio Integration to Mel-scale Mel Frequency Time

  17. Feature Extraction for Speech/Audio Integration to Mel-scale Frequency Log + DCT Time

  18. Feature Extraction for Speech/Audio Conversion to features - Mel frequency cepstral coefficients (MFCC) Frequency Time

  19. 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.

  20. Face Images (Assignment) Normal Lighting Conditions Occlusion

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