Rice’s characteristic function method of analysis for combinations of signals and noise in a memoryless nonlinear system is extended in this paper to greatly facilitate numerical methods of solutions. This improvement is made by describing the nonlinearity as a Fourier series instead of a Fourier transform, as in the original method, thereby producing expressions for calculating the desired output correlation functions as summations rather than double or triple improper integrals that must be estimated. Even with modern computing tools, it has been found that estimating the values of the former improper integrals can be problematic for SNR conditions of particular interest that motivate the use of the characteristic function method, producing unreliable results and prompting researchers to look elsewhere for a solution. The modified method presented in this paper makes this powerful analytical tool more accessible to researchers and engineers, particularly as new semiconductor devices are under development requiring noise analysis. The extended method retains the useful properties of the original, including applicability to one or more signals (sine waves) and to any noise distribution since its characteristic function always exists, particularly Gaussian or random-telegraph shot noise. An alternative fundamental formula for the characteristic function method is presented expressed in terms of the Fourier coefficients and a discrete parameterization of the general characteristic function. New equations are presented and some numerical results for an example nonlinearity with a sinusoid plus Gaussian noise. The new procedure is concisely summarized for application to other problems.