Comparison of standard low pass filter types in two-path half-band IIR filter structures

Two-path half-band recursive filters are a standard structure used to realize efficient up-sampling or down-sampling filtering tasks [1]. In the most conventional implementation the two path filters form quadrature mirror filters offering simultaneous low-pass and high-pass characteristics from the sum and difference of the two paths. These filters are called self reciprocal (SR) and can be a Butterworth filter or an elliptic filter with coupled pass-band and stop-band ripple levels. The two path structure can also be used to implement Tchebyshev-I, Tchebyshev-II, and arbitrary ripple Elliptic filters. The latter options are not self reciprocal and require more arithmetic operations than do the SR options. In this paper we examine and compare the full set half band recursive filter types.