A General Class of Discrete Time-Invariant Filters

where fj is the value of a polynomial f(t) at t = jh, and {Nj} is a stationary (wide-sense) noise sequence of zero mean and known autocorrelation function, 0j . In all that follows, f(t) is assumed to be a fixed, but arbitrary polynomial of degree not exceeding P. We will investigate a certain class of time invariant filters for which the output {x;} is obtained from the input by means of the convolution