Discrete Transforms

The analysis of signals and systems using transform methods is a very important aspect of the examination of processes and problems in an increasingly wide range of applications. Whereas the initial impetus in the development of methods appropriate for handling discrete sets of data occurred mainly in an electrical engineering context (for example in the design of digital filters), the same techniques are in use in such disciplines as cardiology, optics, speech analysis and management, as well as in other branches of science and engineering. This text is aimed at a readership whose mathematical background includes some acquaintance with complex numbers, linear differen­ tial equations, matrix algebra, and series. Specifically, a familiarity with Fourier series (in trigonometric and exponential forms) is assumed, and an exposure to the concept of a continuous integral transform is desirable. Such a background can be expected, for example, on completion of the first year of a science or engineering degree course in which transform techniques will have a significant application. In other disciplines the readership will be past the second year undergraduate stage. In either case, the text is also intended for earlier graduates whose degree courses did not include this type of material and who now find themselves, in a professional capacity, requiring a knowledge of discrete transform methods. Front Matter....Pages i-xii Fourier series, integral theorem, and transforms: a review....Pages 1-24 The Fourier transform. Convolution of analogue signals....Pages 25-53 Discrete signals and transforms. The Z-transform and discrete convolution....Pages 54-90 Difference equations and the Z-transform....Pages 91-116 The discrete Fourier transform....Pages 117-140 Simplification and factorization of the discrete Fourier transform matrix....Pages 141-155 Fast Fourier transforms....Pages 156-177 Back Matter....Pages 178-187 This is an introduction to discrete transform techniques for engineering and science students who have completed the first year of their degree courses. The textbook assumes a familiarity with Fourier series, although a review of the basic theory is provided to assist readers This text provides a thorough introduction to discrete transform techniques aimed at engineering students. Worked examples and illustrations are provided throughout the text to enable readers to relate the techniques to practical engineering problems