Transforms and Fast Algorithms for Signal Analysis and Representations

Transforms have diverse applications in digital signal processing and other areas of science, engineering, and technology. Indeed, new transforms are continuously emerging to solve many new or open problems created by technological advances. To improve the implementation of these transforms, fast algorithms have been created and widely used over the last forty years. Although closely related to the discrete Fourier transform, novel fast algorithms for various transforms have to be developed separately in order to minimize computational complexity and implementation costs.

This book is a comprehensive presentation of results and recent progress on several commonly used transforms and their fast algorithms. In many cases, additional options are provided for new or improved fast algorithms, some not yet well known in the digital signal processing community. Demonstrated throughout the work is the potential for fast algorithms to meet the demands created by fast computing processors, which may lead to advances in modern applications.

Features and Topics:

* Systematic presentation of many new fast algorithms for widely used one-dimensional or multi-dimensional transforms such as the discrete Fourier, discrete Hartley, and discrete cosine transforms

* Improvements on multi-dimensional integer transforms and fast algorithms important for wireless applications

* Comprehensive information on newly created time-frequency transforms to improve resolution of signal representations in the time-frequency domain

* Recent theoretical developments on polynomial transform-based algorithms

* End-of chapter examples, summaries, and references

The work is suitable as a textbook for senior undergraduate and graduate students; it may also be used as a self-study reference for electrical engineers and applied mathematicians working in the fields of electronics, signal, image and speech processing, or digital design and communication.