In the third section we treat the design of halfband-filters with approximately linear phase. By coupling an appropriately designed allpass of even degree n A with a delay of order m=n A ±1 we obtain the desired solution by solving a corresponding approximation problem for the phase of the allpass. The resulting lowpass and highpass are strictly as well as power complementary! The kind of approximation will be done in the sense of maximal flatness, where a closed form solution exists , or in the sense of Chebychev, where the solution is obtained iteratively . The design of systems with minimum phase is presented in section 4. The resulting lowpass and highpass are power complementary. Closed form solutions yield Butterworth and Cauer filters, if a maximal flat or a Chebychev approximation is desired. In all cases a fixed relation exists between the passband frequency Ο P and the tolerated deviation δ P in the passband when the degree n has been chosen.
Document Type: Original Article
Affiliations: 1: Lehrstuhl für Nachrichtentechnik I, Universität Erlangen-Nürnberg, Cauerstraße 7, D-91058 Erlangen, Germany. E-mail: [email protected] 2: Lehrstuhl für Nachrichtentechnik I, Universität Erlangen-Nürnberg, Cauerstraße 7, D-91058 Erlangen, Germany. E-mail: [email protected]
Publication date: 01 December 2001