Mathematical Methodology for Analysis of the Adaptive A/D Converter in Combined CW and Gaussian Interference

The purpose of the present study, a companion paper to that presented by F. Amoroso on Adaptive A/D Converter Performance, is to provide the mathematical basis for the results described in the earlier paper. Emphasis is placed on several algorithms for computation of the distribution function, F(X), of combined CW and Gaussian noise via Fast Fourier Transform and Gaussian quadrature methods, and an explicit series representation of F(X) is provided in terms of gamma and confluent hypergeometric functions. The methodology for relating F(X) to conversion gain, Gc, which is the basic performance measure for the A/D converter, is also explored.