EAN: 9783031013997

SYNTHESIS LECTURES ON SIGNAL PROCESSING THE T...

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 statistical signal processing. Although prediction is only a part of the more
general topics of linear estimation  filtering  and smoothing  this book focuses on linear
prediction. This has enabled detailed discussion of a number of issues that are normally not
found in texts. For example  the theory of vector linear prediction is explained in
considerable detail and so is the theory of line spectral processes. This focus and its small
size make the book different from many excellent texts which cover the topic  including a few
that are actually dedicated to linear prediction. There are several examples and computer-based
demonstrations of the theory. Applications are mentioned wherever appropriate  but the focus is
not on the detailed development of these applications. The writing style is meant to be
suitable for self-study as well as for classroom use at the senior and first-year graduate
levels. The text is self-contained for readers with introductory exposure to signal processing
random processes  and the theory of matrices  and a historical perspective and detailed outline
are given in the first chapter.Table of Contents: Introduction   The Optimal Linear Prediction
Problem   Levinson's Recursion   Lattice Structures for Linear Prediction   Autoregressive
Modeling   Prediction Error Bound and Spectral Flatness   Line Spectral Processes   Linear
Prediction Theory for Vector Processes   Appendix A: Linear Estimation of Random Variables   B:
Proof of a Property of Autocorrelations   C: Stability of the Inverse Filter   Recursion
Satisfied by AR Autocorrelations

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