Equivalence between the extended window design of IIR filters and least squares frequency domain designs

Abstract

A new look at the problem of digitizing analog filters is taken in the light of the proof of the equivalence between weighted least squares (WLS) frequency-domain methods and a previously proposed interpolation-based method referred to as the extended window design (EWD). This equivalence is used to prove new properties of the EWD and WLS methods. First, the EWD filters are shown to be near-optimal due to their equivalence to the WLS filters. Next, improved WLS filter designs are obtained, justified by typical properties of the interpolation method that generates the EWD filters. Thus, the digitizing error can be dramatically reduced by adding a one-or two-step delay and slightly increasing the number of the numerator coefficients relative to the denominator. Finally, a choice of suitable implementations of fractional delay filters is available for the various cases of fixed or variable delays.