This paper presents a solution for the output signal-to-noise ratio of a bandpass nonlinearity which is attractive for numerical evaluations of certain nonlinearities of interest. The solution is obtained by solving a differential equation which results in an expression for thenth order Chebyshev transform of an odd-order nonlinearity in terms of the(n - 1)st-order Chebyshev transform of the derivative of the nonlinearity. The particular cases treated included a linear-logarithmic amplifier, an arctangent limiter, and a piecewise-linear limiter. The approach and results are related to previous efforts.