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The great advancements in the design of microchips, digital systems, and computer hardware over the past 40 years have given birth to digital signal processing (DSP) which has grown over the years into a ubiquitous, multifaceted, and indispensable subject of study. As such DSP has been applied in most disciplines ranging from engineering to economics and from astronomy to molecular biology. Consequently, it would take a multivolume encyclopedia to cover all the facets, aspects, and ramifications of DSP, and such a treatise would require many authors. This textbook focuses instead on the fundamentals of DSP, namely, on the representation of signals by mathematical models and on the processing of signals by discrete-time systems. Various types of processing are possible for signals but the processing of interest in this volume is almost always linear and it typically involves reshaping, transforming, or manipulating the frequency spectrum of the signal of interest. The prerequisite knowledge for the book is a typical undergraduate mathematics background of calculus, complex analysis, and simple differential equations. At certain universities, complex analysis may not be included in the curriculum. To overcome this difficulty, the basics of complex analysis are summarized in Appendix A which can also serve as a quick reference or refresher.