Foreword

Fast signal transforms play a key role in signal processing. They are used in all processing stages, from signal representation to signal restoration and data recovery, to signal encoding for storage and transmission, to feature extraction and decision-making. Of special importance are fast transforms that originate from Fast Fourier Transform.

The purpose of this book is to provide a single source that covers fast transform algorithms, analyses, and applications. It is the result of the collaboration by the author with others in the university community and has been accumulated from time to time over the author’s working lifetime of about 40 years. It now resulted 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. It seemed to me that the nice results in the book of Professor Yaroslavsky book should be better known.

The aim is not to provide a handbook of solutions to particular problems in the areas covered, though some results may be found particularly interesting and useful. More specifically, it is to show how such problems might be tackled and how the technique can be used with ingenuity in a variety of ways.

The book is addressed to a broad circle of experimentalists, researchers and students in experimental sciences that are not regularly educated in signal transforms in various applications ranging from geophysics and astrophysics to metrology and to biomedical engineering. 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.

So, welcome to the transformed land, where life is frequently easier.