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Zero-crossing analysis techniques have long been applied to speech analysis, to automatic speech recognition, and to many other signal-processing and pattern-recognition tasks. In this paper, a mathematical formulation for each of several zero-crossing feature extraction techniques is derived and related (where possible) to each of the other zero-crossing methods. Based upon this mathematical formulation, a physical interpretation of each analysis technique is effected, as is a discussion of the properties of each method. It is shown that four of these methods are a description of a short-time waveform in which essentially the same information is preserved. Each turns out to be a particular normalization of a count of zero-crossing intervals method. The effects of the various forms of normalization are discussed. A fifth method is shown to be a different type of measure; one which preserves information concerning the duration of zero-crossing intervals rather than their absolute number. Although reference is made as to how each of the zero-crossing methods has been applied to automatic speech recognition, an attempt is made to enumerate general characteristics of each of the techniques so as to make the mathematical analysis generally applicable.