Design of narrowband FIR filters with minimal noise gain using complex interpolation

It is shown that polynomial prediction is equivalent to requiring that the transfer function of the predictor interpolates the ´prediction-function´ f (z) = z and its derivatives at z = 1. This result is generalized to all other linear filtering operations, including interpolation, differentiation and smoothing, and to all other narrowband signal models, i.e. polynomially modulated complex exponential signals. An algorithm for determining the coefficients of this type of FIR filter with minimum noise gain is presented and illustrated by deriving the coefficients of predictive differentiators.