A pole-radius-varying IIR notch filter with enhanced post-transient performance

In many applications of notch filters, high quality factor and short transient duration are simultaneously desired. Being contradictory in nature these two requirements pose design challenges. This paper presents an innovative application of a hyperbolic tangent sigmoid (HTS) function to vary the time-varying pole-radius (TVPR) of the pole-zero-constrained (PZC) IIR notch filter to optimally attain these two requirements together. Application of HTS function has allowed the pole-radius to maintain its desired minimum value during the initial phase of filtering, leading to faster transient suppression. This is followed by a steep rise in the pole-radius which allowed the notch filter to attain its desired quality factor soon after the transient suppression was achieved. Therefore, prime emphasis of the proposed notch filter design approach is on the significant reduction of the duration during which pole-radius makes a transition from its minimum to maximum designed values. The performance of proposed notch filter was assessed for transient suppression and selectivity responses in addition to removal of the power line interference from an ECG signal in the LabVIEW™ based simulation and hardware implementation environment. Based on significant improved performances over recent reported exponential TVPR PZC IIR notch filter in all the presented investigations, it is concluded that the proposed design is a better candidate for enhancing the post-transient performance of IIR PZC notch filter.