Fourier and Laplace Transforms

This book presents in a unified manner the fundamentals of both continuous and discrete versions of the Fourier and Laplace transforms. These transforms play an important role in the analysis of all kinds of physical phenomena. As a link between the various applications of these transforms the authors use the theory of signals and systems, as well as the theory of ordinary and partial differential equations. The book is divided into four major parts: periodic functions and Fourier series, non-periodic functions and the Fourier integral, switched-on signals and the Laplace transform, and finally the discrete versions of these transforms, in particular the Discrete Fourier Transform together with its fast implementation, and the z-transform. Each part closes with a separate chapter on the applications of the specific transform to signals, systems, and differential equations. The book includes a preliminary part which develops the relevant concepts in signal and systems theory and also contains a review of mathematical prerequisites.

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