Mitigating in Band Overshoot in Digital High-Pass Filters: Design and Analysis of Bessel and Gaussian Filters for Maximally Flat Step Response

Digital high-pass filters play an important role in transcending the low-frequency noise to maintain the signal integrity in several modern applications of communication systems. The most important distinction between them is the attempt to obtain a flat step response and a minimum of distortion in the amplitude-frequency response (AFR). The trade-off between flat step response and the minimum amplitude-frequency response distortion in IIR high-pass filters generated by bilinear transformations of Bessel and Gaussian low-pass prototypes is explored in this paper. The proposed design uses a parallel structure, subtracting the amplitude-frequency response of the low-pass filter from the direct pass AFR to eliminate step response overshoot without sacrificing time-domain flatness. Filter performance is validated and overshoot behavior quantified using numerical evaluations performed in the Mathcad environment. Comparison of various filter orders in parallel and stage-by-stage connections shows that Gaussian-based HPFs have minimal negative step overshoot (as low as –0.002%) compared to Bessel-based filters (e.g., –0.37% for 8th order). However, AFR overshoot increases with order (72% for Gaussian, 78% for Bessel). The parallel scheme reduces the AFR overshoot by up to 30% over the conventional schemes without degradation in transient response and results in robust low-distortion filters in real-time detection applications.