Linear prediction

About: Linear prediction is a research topic. Over the lifetime, 4495 publications have been published within this topic receiving 115308 citations.

Adaptive Filter Theory

Abstract: Background and Overview. 1. Stochastic Processes and Models. 2. Wiener Filters. 3. Linear Prediction. 4. Method of Steepest Descent. 5. Least-Mean-Square Adaptive Filters. 6. Normalized Least-Mean-Square Adaptive Filters. 7. Transform-Domain and Sub-Band Adaptive Filters. 8. Method of Least Squares. 9. Recursive Least-Square Adaptive Filters. 10. Kalman Filters as the Unifying Bases for RLS Filters. 11. Square-Root Adaptive Filters. 12. Order-Recursive Adaptive Filters. 13. Finite-Precision Effects. 14. Tracking of Time-Varying Systems. 15. Adaptive Filters Using Infinite-Duration Impulse Response Structures. 16. Blind Deconvolution. 17. Back-Propagation Learning. Epilogue. Appendix A. Complex Variables. Appendix B. Differentiation with Respect to a Vector. Appendix C. Method of Lagrange Multipliers. Appendix D. Estimation Theory. Appendix E. Eigenanalysis. Appendix F. Rotations and Reflections. Appendix G. Complex Wishart Distribution. Glossary. Abbreviations. Principal Symbols. Bibliography. Index.

Linear prediction: A tutorial review

Abstract: This paper gives an exposition of linear prediction in the analysis of discrete signals The signal is modeled as a linear combination of its past values and present and past values of a hypothetical input to a system whose output is the given signal In the frequency domain, this is equivalent to modeling the signal spectrum by a pole-zero spectrum The major part of the paper is devoted to all-pole models The model parameters are obtained by a least squares analysis in the time domain Two methods result, depending on whether the signal is assumed to be stationary or nonstationary The same results are then derived in the frequency domain The resulting spectral matching formulation allows for the modeling of selected portions of a spectrum, for arbitrary spectral shaping in the frequency domain, and for the modeling of continuous as well as discrete spectra This also leads to a discussion of the advantages and disadvantages of the least squares error criterion A spectral interpretation is given to the normalized minimum prediction error Applications of the normalized error are given, including the determination of an "optimal" number of poles The use of linear prediction in data compression is reviewed For purposes of transmission, particular attention is given to the quantization and encoding of the reflection (or partial correlation) coefficients Finally, a brief introduction to pole-zero modeling is given

Digital Signal Processing: Principles, Algorithms, and Applications

Abstract: 1. Introduction. 2. Discrete-Time Signals and Systems. 3. The Z-Transform and Its Application to the Analysis of LTI Systems. 4. Frequency Analysis of Signals and Systems. 5. The Discrete Fourier Transform: Its Properties and Applications. 6. Efficient Computation of the DFT: Fast Fourier Transform Algorithms. 7. Implementation of Discrete-Time Systems. 8. Design of Digital Filters. 9. Sampling and Reconstruction of Signals. 10. Multirate Digital Signal Processing. 11. Linear Prediction and Optimum Linear Filters. 12. Power Spectrum Estimation. Appendix A. Random Signals, Correlation Functions, and Power Spectra. Appendix B. Random Numbers Generators. Appendix C. Tables of Transition Coefficients for the Design of Linear-Phase FIR Filters. Appendix D. List of MATLAB Functions. References and Bibliography. Index.

Linear Prediction of Speech

Abstract: 1. Introduction.- 1.1 Basic Physical Principles.- 1.2 Acoustical Waveform Examples.- 1.3 Speech Analysis and Synthesis Models.- 1.4 The Linear Prediction Model.- 1.5 Organization of Book.- 2. Formulations.- 2.1 Historical Perspective.- 2.2 Maximum Likelihood.- 2.3 Minimum Variance.- 2.4 Prony's Method.- 2.5 Correlation Matching.- 2.6 PARCOR (Partial Correlation).- 2.6.1 Inner Products and an Orthogonality Principle.- 2.6.2 The PARCOR Lattice Structure.- 3. Solutions and Properties.- 3.1 Introduction.- 3.2 Vector Spaces and Inner Products.- 3.2.1 Filter or Polynomial Norms.- 3.2.2 Properties of Inner Products.- 3.2.3 Orthogonality Relations.- 3.3 Solution Algorithms.- 3.3.1 Correlation Matrix.- 3.3.2 Initialization.- 3.3.3 Gram-Schmidt Orthogonalization.- 3.3.4 Levinson Recursion.- 3.3.5 Updating Am(z).- 3.3.6 A Test Example.- 3.4 Matrix Forms.- 4. Acoustic Tube Modeling.- 4.1 Introduction.- 4.2 Acoustic Tube Derivation.- 4.2.1 Single Section Derivation.- 4.2.2 Continuity Conditions.- 4.2.3 Boundary Conditions.- 4.3 Relationship between Acoustic Tube and Linear Prediction.- 4.4 An Algorithm, Examples, and Evaluation.- 4.4.1 An Algorithm.- 4.4.2 Examples.- 4.4.3 Evaluation of the Procedure.- 4.5 Estimation of Lip Impedance.- 4.5.1 Lip Impedance Derivation.- 4.6 Further Topics.- 4.6.1 Losses in the Acoustic Tube Model.- 4.6.2 Acoustic Tube Stability.- 5. Speech Synthesis Structures.- 5.1 Introduction.- 5.2 Stability.- 5.2.1 Step-up Procedure.- 5.2.2 Step-down Procedure.- 5.2.3 Polynomial Properties.- 5.2.4 A Bound on |Fm(z)|.- 5.2.5 Necessary and Sufficient Stability Conditions.- 5.2.6 Application of Results.- 5.3 Recursive Parameter Evaluation.- 5.3.1 Inner Product Properties.- 5.3.2 Equation Summary with Program.- 5.4 A General Synthesis Structure.- 5.5 Specific Speech Synthesis Structures.- 5.5.1 The Direct Form.- 5.5.2 Two-Multiplier Lattice Model.- 5.5.3 Kelly-Lochbaum Model.- 5.5.4 One-Multiplier Models.- 5.5.5 Normalized Filter Model.- 5.5.6 A Test Example.- 6. Spectral Analysis.- 6.1 Introduction.- 6.2 Spectral Properties.- 6.2.1 Zero Mean All-Pole Model.- 6.2.2 Gain Factor for Spectral Matching.- 6.2.3 Limiting Spectral Match.- 6.2.4 Non-uniform Spectral Weighting.- 6.2.5 Minimax Spectral Matching.- 6.3 A Spectral Flatness Model.- 6.3.1 A Spectral Flatness Measure.- 6.3.2 Spectral Flatness Transformations.- 6.3.3 Numerical Evaluation.- 6.3.4 Experimental Results.- 6.3.5 Driving Function Models.- 6.4 Selective Linear Prediction.- 6.4.1 Selective Linear Prediction (SLP) Algorithm.- 6.4.2 A Selective Linear Prediction Program.- 6.4.3 Computational Considerations.- 6.5 Considerations in Choice of Analysis Conditions.- 6.5.1 Choice of Method.- 6.5.2 Sampling Rates.- 6.5.3 Order of Filter.- 6.5.4 Choice of Analysis Interval.- 6.5.5 Windowing.- 6.5.6 Pre-emphasis.- 6.6 Spectral Evaluation Techniques.- 6.7 Pole Enhancement.- 7. Automatic Formant Trajectory Estimation.- 7.1 Introduction.- 7.2 Formant Trajectory Estimation Procedure.- 7.2.1 Introduction.- 7.2.2 Raw Data from A(z).- 7.2.3 Examples of Raw Data.- 7.3 Comparison of Raw Data from Linear Prediction and Cepstral Smoothing.- 7.4 Algorithm 1.- 7.5 Algorithm 2.- 7.5.1 Definition of Anchor Points.- 7.5.2 Processing of Each Voiced Segment.- 7.5.3 Final Smoothing.- 7.5.4 Results and Discussion.- 7.6 Formant Estimation Accuracy.- 7.6.1 An Example of Synthetic Speech Analysis.- 7.6.2 An Example of Real Speech Analysis.- 7.6.3 Influence of Voice Periodicity.- 8. Fundamental Frequency Estimation.- 8.1 Introduction.- 8.2 Preprocessing by Spectral Flattening.- 8.2.1 Analysis of Voiced Speech with Spectral Regularity.- 8.2.2 Analysis of Voiced Speech with Spectral Irregularities.- 8.2.3 The STREAK Algorithm.- 8.3 Correlation Techniques.- 8.3.1 Autocorrelation Analysis.- 8.3.2 Modified Autocorrelation Analysis.- 8.3.3 Filtered Error Signal Autocorrelation Analysis.- 8.3.4 Practical Considerations.- 8.3.5 The SIFT Algorithm.- 9. Computational Considerations in Analysis.- 9.1 Introduction.- 9.2 Ill-Conditioning.- 9.2.1 A Measure of Ill-Conditioning.- 9.2.2 Pre-emphasis of Speech Data.- 9.2.3 Prefiltering before Sampling.- 9.3 Implementing Linear Prediction Analysis.- 9.3.1 Autocorrelation Method.- 9.3.2 Covariance Method.- 9.3.3 Computational Comparison.- 9.4 Finite Word Length Considerations.- 9.4.1 Finite Word Length Coefficient Computation.- 9.4.2 Finite Word Length Solution of Equations.- 9.4.3 Overall Finite Word Length Implementation.- 10. Vocoders.- 10.1 Introduction.- 10.2 Techniques.- 10.2.1 Coefficient Transformations.- 10.2.2 Encoding and Decoding.- 10.2.3 Variable Frame Rate Transmission.- 10.2.4 Excitation and Synthesis Gain Matching.- 10.2.5 A Linear Prediction Synthesizer Program.- 10.3 Low Bit Rate Pitch Excited Vocoders.- 10.3.1 Maximum Likelihood and PARCOR Vocoders.- 10.3.2 Autocorrelation Method Vocoders.- 10.3.3 Covariance Method Vocoders.- 10.4 Base-Band Excited Vocoders.- 11. Further Topics.- 11.1 Speaker Identification and Verification.- 11.2 Isolated Word Recognition.- 11.3 Acoustical Detection of Laryngeal Pathology.- 11.4 Pole-Zero Estimation.- 11.5 Summary and Future Directions.- References.

Statistical signal processing : detection, estimation, and time series analysis

Abstract: 1. Introduction. 2. Rudiments of Linear Algebra and Multivariate Normal Theory. 3. Sufficiency and MVUB Estimators. 4. Neyman-Pearson Detectors. 5. Bayes Detectors. 6. Maximum Likelihood Estimators. 7. Bayes Estimators. 8. Minimum Mean-Squared Error Estimators. 9. Least Squares. 10. Linear Prediction. 11. Modal Analysis.