The book covers fast transform algorithms and applications in signal and image processing.

What is it about?

The book contains basics of the theory of signal transforms, comprehensively reviews of Discrete Fourier Transforms (DFT) and their different modification, such as Discrete Cosine Transform, Shifted, Scaled and rotated DFTs, binary transforms, such as Walsh-Hadamard and Haar Transforms, Wavelet Transforms and multi-resolution analysis, sliding window transforms and "time-frequency" signal representation, Radon Traqnsform. Among applications considered signal numerical spectrum analysis, signal/image restoration, signal/image precise interpolation, re-sampling, differentiation and integration. Reviewed are also corresponding efficient computational algorithms.

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Why is it important?

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