On the mean-square noise power of an optimum continuous filter for correlated noise

This paper presents the equations for the mean-square error of the output of a continuous finite memory filter. The filter output error is unbiased for arbitrary input polynomials up to degree
n
, and has minimum variance. The input is taken as a polynomial of degree
n
plus random stationary noise. Noise processes are considered, 1) where the noise is exponentially correlated, and 2) in the white noise case. The solution for a desired output which is an arbitrary fixed linear operation on the input polynomial is given. Tables and graphs of the mean-square error for the derivative and prediction operator for the 0th, 1st, and 2nd derivatives are presented, and for input polynomials up to the 6th degree.