Multiple IIR notch filter design and optimization by Secant approximation

Cascading single notch filters is the usual way to construct a multiple notch filter. However, the cascading connection may introduce the uncontrollable non-unity passband gains between notch frequencies. In other words, when the pole placement of a multiple notch filter is changed, the exact notch frequencies between the notch frequencies may not be precisely controlled. To compensate this effect, the design of IIR multiple notch filters with controllable passband gain is concerned. One of the solutions was an allpass based design using the pole-reposition technique which is proposed by Thamrongmas et al. Even this technique was simple, however, it requires high number of iterations to find the optimal design parameter that makes the passband gains (between two notch frequencies) be uniformly flat. In this paper, the Secant method is applied to improve the performance of the optimal search algorithm. The result shows the significantly faster search i.e. the algorithm often converges within fewer than 10 iterations.