Pole-Zero Assignment of All-Pass-Based Notch Filters

Abstract

In this brief, a new technique for designing the all-pass-based notch filter is proposed. An all-pass-based notch filter consists of an all-pass filter, which has the mirror-image symmetry relation between the numerator and denominator polynomials. With this property, a relationship between the pole angel and the zero angle of an all-pass-based notch filter is derived. Knowing this relationship, we can design an all-pass-based notch filter by assigning the pole position according to the zero position. The process of the new technique is illustrated in this brief. Moreover, experiments are presented to examine a track of the pole position at the specific frequency and to demonstrate a design example of an all-pass-based notch filter.