Spectral analysis of order statistic filters

We analyze the effect of filter coefficient selection on the power spectral density of an order statistic filtered signal. Assuming that the input signal is a sequence of independent and identically distributed random variates, the autocovariance and the power spectrum of the output are computed. These PSDs are compared with those of the corresponding linear finite impulse response filters with identical coefficients. It is found that, in general, low frequency components predominate regardless of coefficient selection, suggesting an inherent smoothing in the ordering process.