The theory of linear prediction

• Main Author: Vaidyanathan, P. P.
• Format: Electronic
• Language: English
• Published: San Rafael, Calif. (1537 Fourth Street, San Rafael, CA 94901 USA) : Morgan & Claypool Publishers, c2008.
• Series: Synthesis lectures on signal processing (Online), #3.
• Subjects: Prediction theory.
• Online Access: Abstract with links to full text

Linear prediction theory has had a profound impact in the field of digital signal processing. Although the theory dates back to the early 1940s, its influence can still be seen in applications today. The theory is based on very elegant mathematics and leads to many beautiful insights into statistica...

Table of Contents:

• 1. Introduction
• 1.1. History of linear prediction
• 1.2. Scope and outline
• 2. The optimal linear prediction problem
• 2.1. Introduction
• 2.2. Prediction error and prediction polynomial
• 2.3. The normal equations
• 2.4. Properties of the autocorrelation matrix
• 2.5. Estimating the autocorrelation
• 2.6. Concluding remarks
• 3. Levinson's recursion
• 3.1. Introduction
• 3.2. Derivation of Levinson's recursion
• 3.3. Simple properties of Levinson's recursion
• 3.4. The whitening effect
• 3.5. Concluding remarks
• 4. Lattice structures for linear prediction
• 4.1. Introduction
• 4.2. The backward predictor
• 4.3. Lattice structures
• 4.4. Concluding remarks
• 5. Autoregressive modeling
• 5.1. Introduction
• 5.2. Autoregressive processes
• 5.3. Approximation by an AR(N) processes
• 5.4. Autocorrelation matching property
• 5.5. Power spectrum of the AR model
• 5.6. Application in signal compression
• 5.7. MA and ARMA processes
• 5.8. Summary
• 6. Prediction error bound and spectral flatness
• 6.1. Introduction
• 6.2. Prediction error for an AR process
• 6.3. A measure of spectral flatness
• 6.4. Spectral flatness of an AR process
• 6.5. Case where signal is not AR
• 6.6. Maximum entropy and linear prediction
• 6.7. Concluding remarks
• 7. Line spectral processes
• 7.1. Introduction
• 7.2. Autocorrelation of a line spectral process
• 7.3. Time domain descriptions
• 7.4. Further properties of time domain descriptions
• 7.5. Prediction polynomial of line spectral processes
• 7.6. Summary of properties
• 7.7. Identifying a line spectral process in noise
• 7.8. Line spectrum pairs
• 7.9. Concluding remarks
• 8. Linear prediction theory for vector processes
• 8.1. Introduction
• 8.2. Formulation of the vector LPC problem
• 8.3. Normal equations : vector case
• 8.4. Backward prediction
• 8.5. Levinson's recursion : vector case
• 8.6. Properties derived from Levinson's recursion
• 8.7. Transfer matrix functions in vector LPC
• 8.8. The FIR lattice structure for vector LPC
• 8.9. The IIR lattice structure for vector LPC
• 8.10. The normalized IIR lattice
• 8.11. The paraunitary or MIMO all-pass property
• 8.12. Whitening effect and stalling
• 8.13. Properties of transfer matrices in LPC theory
• 8.14. Concluding remarks
• A. Linear estimation of random variables
• A.1. The orthogonality principle
• A.2. Closed-form solution
• A.3. Consequences of orthogonality
• A.4. Singularity of the autocorrelation matrix
• B. Proof of a property of autocorrelations
• C. Stability of the inverse filter
• D. Recursion satisfied by AR autocorrelations
• Problems
• References
• Author biography
• Index.