Measurement of the probability density function of communication signals

A method for estimating and measuring the probability density function (PDF) of random signals is derived. The method is based on a new representation of P.M. Woodward's theorem (1952), and has been tested in practice with good results. A new proof of Woodward's theorem is presented which includes the linear mean-square estimator and an upper bound on the error of the estimation based on Papoulis' inequality. The experimental setup for measuring the PDF is a simple one, consisting of a frequency modulation and a spectrum analyzer. The theory assures an error smaller than 0.08% for a modulating index of ten or more.<
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