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Chapter 12:
Applications Involving Hypergeometric-Type Functions
12.1 Introduction In this final chapter we illustrate the use of the general family of hypergeometric functions in various applications. Although we have chosen specific examples from the fields of statistical communication theory, fluid mechanics, and random fields, the techniques we use are sufficiently general that they apply to a wider range of applications. As before, we assume only a working knowledge of the subjects in order to follow the exposition. 12.2 Statistical Communication Theory Communication systems may be broadly classified in terms of linear operations, such as amplification and filtering, and nonlinear operations, such as modulation and detection. Random noise, which appears at the input to any communications receiver, interferes with the reception of incoming radio and radar signals. When this noise is channeled through a passband linear filter whose bandwidth is narrow compared with the center frequency ω 0 of the filter, the output is called narrowband noise and has the representation (recall Sec. 8.3.1) n(t)=x(t)cosω 0 t−y(t)sinω 0 t where x(t) and y(t) are independent gaussian (or normal) random processes with zero means and equal mean-squared values N.
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