On the mean-square noise power of an optimum linear digital filter for correlated noise input

An asymptotic solution for the mean-square output noise power of an optimum digital filter is obtained. It is assumed that the input consists of a polynomial plus correlated noise. The asymptotic solution is found by fixing the interval between samples and allowing the number of samples to approach infinity. The solution obtained for the minimum variance filter is compared with the solution as obtained for the "least-squares filter," and it is shown that the latter filter is asymptotically efficient as compared to the former. It is shown for each of the above filters that the mean-square output noise power is proportional to the spectral density function of the correlated noise, evaluated at zero frequency, and that the factor of proportionality is the same.