Phase-Compensated Time-Varying Butterworth Filters

Abstract

One of the important problems of signal processing is to design the filters which possess linear phase characteristics. This paper presents the concept of time-varying Butterworth filters with linear phase. The compensation of the phase characteristics is carried out with the aid of phase shifter which is cascade-connected to the structure of the original Butterworth filter given by the transfer function. The parameters of the phase shifter were calculated in this way that the group delay of the designed filter is possible constant in the filter pass-band. Time varying coefficients were introduced to the phase-compensated filter structure for the purpose of minimization of the filter transient state. This paper contains simulation results of proposed filters and comparison with classic circuits.

An Efficient Method of Group Delay Equalization for Digital IIR Filters

“…To counter the effect of non-constant group delay one can find fine methods that were used with continuous-time filters [6][7][8][9]. Unfortunately, the proposed approaches cannot be fully put to discrete systems using simple transformations (e.g.…”

Models of Continuous-Time Linear Time-Varying Systems with Fully Adaptable System Modes

“…As it will be seen soon, the proposed functions represent the best alternative to build a system based on equation (11) with complex dynamical behaviour. In previous work (Kaszyński, 2003;Jaskula, & Kaszyński, 2004;Piskorowski, 2006), the following equation was proposed for defining a new class of low-pass time-varying filters…”

A novel concept of phase-compensated continuous-time filters

“…Since the Butterworth approximation guarantees the stability of the timeinvariant filter, and Q > 0 and x 0p > 0 guarantee the stability of the allpass filter [3], one can skip the stability issue for the parametric filter. The best results in the reduction of the transient state of compensated Butterworth filters were obtained when the parameters x 0i , 1 T , and x 0p were varied according to the same function F(t) (with the same variation range denoted by d x ), while b and b p were varied according to the different functions (with different variation ranges denoted d b and d b p , respectively). b(t) causes stronger damping in the initial phase of the filter work, and the suppression of undesirable overshoot in the step response, and b p (t) eliminates the undershoot from the step response.…”

“…This paper is an updated and extended version of [1] and presents a novel approach to phase-compensated analog filters by using the time-varying parameters technique. In Sect.…”