Output Autocorrelation Functions of Smooth and Hard Limiters†

For a stationary Gaussian input, the output autocorrelation functions of the full-wave smooth and hard limiters are derived by applying Blaehman's (1964) technique. A new method is used, in conjunction with Plackett's (1954) reduction formula for the case of four Gaussian variates, to evaluate the probability that these variates are positive, when their covariance matrix is of a specific form. On combining this method with Blaehman's technique, the autocorrelation functions of the half-wave smooth and hard limiters are derived in terms of the dilogarithm function and its real part, both of which have been studied and tabulated.