Wiener-like orthogonal functional expansions may be constructed with respect to test ensembles that are non-Gaussian, non-white, or both. Although the original Wiener expansion has particularly-advantageous analytical properties, orthogonal expansions constructed with respect to other ensembles have practical advantages for laboratory implementation. We show how functional expansions based on two classes of input ensembles -- white but non-Gaussian discrete noises and the sum of sinusoids -- converge to the standard Wiener kernels. For discrete noises, the disparity between the standard and non-standard kernels of a linear-static nonlinear transducer is proportional to the kurtosis of the input signal and inversely proportional to the ratio of the integration time of the linear filter to the time-discretization. For the sum of sinusoids, the disparity is inversely proportional to the effective number of sinusoids passed by the initial linear stage.