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Research Article |

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

Author(s): Hussein Shakor Mogheer1, Alrubei Mohammed A.T2, Yassir AL-Karawi3

Published In : International Journal of Electrical and Electronics Research (IJEER)        Volume 13, Issue 3

Publisher : FOREX Publication

Published : 30 September 2025

e-ISSN : 2347-470X

Page(s) : 536-546

DOI: https://doi.org/10.37391/IJEER.130318

Abstract

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.

Keywords: AFR overshoot, Bessel and Gaussian filters, Bilinear transformation, Digital high-pass filters (HPFs), Group delay, Step response, In-band frequency overshoot mitigation, Maximally flat step response.




Hussein Shakor Mogheer , Research Lecture, Department of Communication Engineering, College of Engineering, University of Diyala, Baqubah 32001, Iraq

Alrubei Mohammed A.T, Assistant Professor, Department of Electronics and Communication Techniques, Al-Najaf Technical Institute, Al-Furat Al-Awsat Technical University, Najaf 54001, Iraq

Yassir AL-Karawi, Assistant Professor, Department of Communication Engineering, College of Engineering, University of Diyala, Baqubah 32001, Iraq;

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Hussein Shakor Mogheer, Alrubei Mohammed A.T., Yassir AL-Karawi(2025), Mitigating in Band Overshoot in Digital High-Pass Filters: Design and Analysis of Bessel and Gaussian Filters for Maximally Flat Step Response. IJEER 13(3), 536-546. DOI: 10.37391/IJEER.130318.