Introduction

This ebook covers fast transform algorithms, analyses, and applications in a single volume. It is the result of the collaboration by the author with others in the world wide university community and has been accumulated over the author’s working lifetime of about 40 years. It has now culminated in a nice mix of theoretical development and practical uses of various fast transforms. Thus readers will find practical approaches not covered elsewhere for the design and development of fast transform methods.

Some of the most immediate applications, such as detection and analysis of periodicities in data, signal denoising and deblurring, signal resampling, precise differentiation and integration are covered and supported by concrete algorithms in this book. Other potential applications are supported by a tour of the theory and mathematical abstraction. The book is addressed to a broad circle of experimentalists, researchers and students that are not regularly educated in signal processing and work in various fields in experimental sciences ranging from physics a to metrology and to biomedical engineering.