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A concise formula is derived for the probability distribution of the instantaneous frequency of an arbitrary bandpass signal plus Gaussian noise. The results are presented in terms of Marcum's <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</tex> -functions, with well-known properties. The results are applicable in the performance analysis of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> -ary FM and PM data transmission systems. Illustrative examples of the application of the formula are worked out for binary FSK.
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Salz et al. (1964) studied this question.
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