A class of infinite-duration impulse response digital filters for sampling rate reduction

Abstract

A new class of recursive digital filters for sampling rate reduction is discussed. These filters present equiripple behavior in the magnitude response, with all their zeros located on the unit circle. These new filters bring together, to some extent, the advantages of finite-duration impulse response (FIR) and elliptic designs by having only powers of z <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</sup> in the denominator (D is the decimation ratio). Only every <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</tex> th output has to be computed, as in the FIR case; while some feedback terms, as in the elliptic case, are also present. The design and some optimality properties of these filters are discussed. Some characteristics of filters with only powers of z <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</sup> in the denominator, such as pole-zero location, group delay, and coefficient sensitivity are discussed and compared with elliptic designs. It is shown how these new filters require significantly fewer multiplications per second than equivalent FIR and elliptic designs.