The Influence of a Band-Stop Filter on the Effectiveness of Linearizing the Analog Band-Pass Filter Phase Frequency Response

Abstract

The previously published works of the authors dealt with methods aimed at linearizing the phase frequency responses of analog filters using digital linearizing finite impulse response (FIR) filters. If the operating frequency band contains narrow-band interference, such interference often needs to be suppressed by using a narrow-band analog band-stop filter. However, when a band-stop filter is connected in series, the linearized phase frequency response may become distorted. The article examines the influence of a narrow-band analog band-stop filter on the effectiveness of linearizing the phase frequency responses of a complex analog band-pass filter using a complex band-pass linearizing digital FIR filter. The study was conducted using a circuit simulation program based on a model consisting of the following modules: a complex analog band-pass filter with a sixth-order Butterworth low-pass filter prototype, a narrow-band complex analog band-stop filter with a third-order Butterworth low-pass filter prototype, and a complex digital band-pass linearizing FIR filter. The article presents the results from studying the frequency band in which the phase frequency response linearity is distorted to an acceptable degree. A sharp change in the group delay time level takes place in the stopband vicinity. The frequency band in which the group delay ripple is larger than the pre-linearization group delay ripple is referred to as the linearization effect loss band. If the difference between the band-stop filter’s passband boundary frequencies is much (by dozens of times) smaller than the band of the complex band-pass filter, the linearization effect is retained over most of the passband. With the selected parameters and orders of the complex analog filter and band-stop filter, the frequency band in which the linearization effect vanishes is approximately seven times greater than the difference between the band-stop filter’s passband boundary frequencies. Such an approach is relevant in filtering narrow-band interference within the frequency band of broadband signals.