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The emphasis of this text is the broad field of Fourier analysis and some of its immediate outgrowths including convolution, systems theory, Shannon sampling theory and the modelling of random variables and stochastic processes. The contents of this book evolved from a set of lecture notes for courses in advanced engineering mathematics (Chapters 2, 3, 4, 12 and 13), multidimensional signal processing (Chapters 2, 9 and 11), signal reconstruction (Chapters 2, 10 and 11) and Shannon sampling and interpolation theory (Chapters 2, 5, 7, 6 and 7). Chapter 4 is useful as a supplement a graduate course on random variables and stochastic processes. The book is written at the level of the advanced senior or first year
graduate student who has an introductory foundation in Fourier analysis and stochastic processes. Rudimentary familiarity with image processing is helpful but not necessary.
The book is written as a text, but can also serve as a handbook or source of material for self study. In order to present material from an alternate point of view and to facilitate self study, solutions to selected problems are included at the end of each chapter. In general, the problems are not designed for linear extension of concepts presented in the text. They are, rather, often used to present new material or to establish concepts from a new viewpoint.
An extensive bibliography is also included