Power-complementary Iir Filter Pairs with an Adjustable Crossover Frequency

Complementary infinite-impulse response (IIR) filter pairs can be synthesized to generate power-complementary, allpass complementary, or magnitude-complementary filter pairs (see, e.g., [1]). A very attractive alternative to generate a power-complementary low-pass/high-pass IIR filter pair is to use lattice wave digital (LWD) filters (parallel connections of two all-pass filters) [2]–[4]. Usually, the intersection for a low-pass/high-pass filter pair occurs in the middle of the base-band, that is, the crossover frequency is located exactly at 1/4 in terms of the normalized frequency. If the stop-band attenuation of both filters is the same, then the low-pass and high-pass filters are both half-band IIR filters (see, e.g., [4]– [5]). This paper introduces a technique to change, by means of simple formulae, the location of the crossover frequency of the half-band filter pair to an arbitrary location while still retaining the attenuation properties of the initial half-band filters. For this purpose, elliptic minimal Q-factors (EMQF) transfer functions introduced in [6]–[8] provide directly the desired solution. In addition to the direct parallel connections of two allpass filters, the structure constructed as a tapped cascaded interconnection of two identical all-pass filters is considered based on the use of the synthesis schemes described in [9]− [12]. This structure allows one to generate powercomplementary filter pairs with an adjustable crossover frequency using very low-order all-pass filters.