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Written using clear and accessible language, this text provides detailed coverage of the core mathematical concepts underpinning signal processing. All the core areas of mathematics are covered, including generalized inverses, singular value decomposition, function representation, and optimization, with detailed explanations of how basic concepts in these areas underpin the methods used to perform signal processing tasks. A particular emphasis is placed on the practical applications of signal processing, with numerous in-text practice questions and real-world examples illustrating key concepts, and MATLAB programs with accompanying graphical representations providing all the necessary computational background. This is an ideal text for graduate students taking courses in signal processing and mathematical methods, or those who want to establish a firm foundation in these areas before progressing to more advanced study.