Introduction to Orthogonal Transforms
With Applications in Data Processing and Analysis

A systematic, unified treatment of orthogonal transform methods that guides the reader from mathematical theory to problem solving in practice.

Ruye Wang (Author)

9780521516884, Cambridge University Press

Hardback, published 8 March 2012

590 pages, 191 b/w illus. 5 tables 117 exercises
25.2 x 17.9 x 3 cm, 1.29 kg

A systematic, unified treatment of orthogonal transform methods for signal processing, data analysis and communications, this book guides the reader from mathematical theory to problem solving in practice. It examines each transform method in depth, emphasizing the common mathematical principles and essential properties of each method in terms of signal decorrelation and energy compaction. The different forms of Fourier transform, as well as the Laplace, Z-, Walsh–Hadamard, Slant, Haar, Karhunen–Loève and wavelet transforms, are all covered, with discussion of how each transform method can be applied to real-world experimental problems. Numerous practical examples and end-of-chapter problems, supported by online Matlab and C code and an instructor-only solutions manual, make this an ideal resource for students and practitioners alike.

1. Signals and systems
2. Vector spaces and signal representation
3. Continuous-time Fourier transform
4. Discrete-time Fourier transform
5. Applications of the Fourier transforms
6. The Laplace and z-transforms
7. Fourier related orthogonal transforms
8. The Walsh–Hadamard, slant and Haar transforms
9. Karhunen–Loeve transform and principal component analysis
10. Continuous and discrete-time wavelet transforms
11. Multiresolution analysis and discrete wavelet transform
Appendix 1. Review of linear algebra
Appendix 2. Review of random variables.

Subject Areas: Signal processing [UYS], Communications engineering / telecommunications [TJK], Electronics & communications engineering [TJ]