The use of adaptive algorithms such as Kalman Filtering, LMS and RLS
together with FIR model structures is very common and extensively
analysed. In the interests of improved performance an
extension of the FIR structure has been proposed
in which the fixed poles are not all at the origin, but instead are chosen
by prior knowledge to be close to where the true poles are.
Existing FIR analysis would indicate that the noise and tracking
properties of such a scheme are invariant to the choice of fixed pole location.
This paper establishes both numerically and theoretically
that in fact this is not the case. Instead, the dependence of fixed
pole location is made explicit by deriving frequency domain
expressions that are obtained by using new results on
generalised Fourier series and generalised Toeplitz matrices.