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Digital filtering is the process of spectrum shaping of signal waveforms, using digital components as the basic dements for implementation. This process is extensively used in the computer simulation of analog filters. The unmistakable trends toward increased speed and decreased cost and size of digital components make digital filtering especially attractive at this time. These trends promise to end the virtual monopoly of analog components for realizing real-time filters. This paper attempts to set the stage for the companion papers on digital filtering to follow in this topical issue. After introducing the z-transform of a discrete-time series, the use of this transform in linear system analysis is considered. The relationship between discrete and continuous signals and systems is then discussed. Since all the papers of this issue are concerned with digital filter implementations in one form or another, only an overview of these implementations is given here. These include filter configurations, design methods, quantization effects, and the fast convolution method for implementing nonrecursive filters.