Transforms and Fast Algorithms for Signal Analysis and Representations

the long version

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.