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This chapter presents a historical overview of the discipline of digital signal processing. Digital signal processing (DSP) is the art of using computer technologies to enhance, analyze, or manipulate images, sounds, radar pulses, and other real-world signals. The chapter discusses two aspects of the conversion process: sampling and aliasing. Sampling changes a continuous-time (CT) signal into a discrete-time (DT) signal, whereas aliasing takes place at two points in the analog-digital-analog conversion process: first during sampling of the input CT signal and then during reconstruction. Special emphasis is given on analog-digital (A/D)-conversion process and the signal-recovery process. The chapter describes the discrete Fourier transform and the algorithms for calculating it efficiently. It introduces two of the most significant DSP operations, digital filtering, and spectrum estimation. It also introduces a simple application of DSP known as frequency-selective filtering and discusses methods of characterizing, specifying, and implementing frequency-selective digital filters. The chapter describes the essential aspects of programmable DSP chips and mentions the various types of software design tools available.