A Multinotch FIR Filter Based on a Stable IIR Filter Prototype with Improved Dynamic Performance via Iterative Determination of Nonzero Initial Conditions Using Vector Projection

In many cases, the removal of individual frequency components from a signal spectrum is achieved using notch and multinotch filters. One of the main disadvantages of such filters is the occurrence of transient states, which depend, among other factors, on the filter order and selectivity, i.e., the bandwidth of the stopband. In this paper, the authors present a method for synthesizing a finite impulse response (FIR) multinotch filter based on a prototype infinite impulse response (IIR) notch filter. The proposed approach is characterized by a significant reduction in the influence of transient effects on the filter response, achieved through the iterative determination of nonzero initial conditions. This allows the dynamic performance of the filter to be improved without compromising its frequency response. Furthermore, the proposed filter structure is characterized by having a lower filter order than conventional filtering structures while maintaining satisfactory filtration quality. To demonstrate the properties of the proposed structure, computer simulations were performed and filtration quality metrics were evaluated. The obtained results indicate that the proposed structure outperforms classical filtering methods by ensuring faster stabilization of the response during the transient state. Moreover, it was demonstrated that the proposed method of reducing the FIR filter order has only a minor effect on filtration quality.