Memoryless Nonlinearities With Gaussian Inputs: Elementary Results

We present elementary derivations of some useful results for memoryless nonlinearities driven by Gaussian noise. The present relations may be obtained as special cases of more general results,1 but the present methods are elementary and give physical understanding. Let a nonlinearity have input jc, output 2, and nonlinear characteristic h(x); 2 = h(x).