Yi Huoping, Chang Fuhao, Tan Ping, Huang Bingqiang, Wu Yongbo, Xu Zhen, Ma Bingyu, Ma Jien
Automation and Electrical Engineering, Zhejiang University of Science and Technology, Hangzhou, 310023, China.
Xianheng International Electrical Manufacturing Co., Ltd, Hangzhou, 310000, China.
Sci Rep. 2025 Apr 1;15(1):11074. doi: 10.1038/s41598-025-87175-5.
Maximally flat digital filters (MFDFs) are widely applied in applications where the energy of useful signals is concentrated around some specific frequencies. A typical design method of MFDFs is to impose constraints on the filter's frequency response and its first- to high-order derivatives at some frequencies and to fully determine the filter coefficients from these constraints. However, infinite impulse response (IIR) MFDFs that are designed by the method are not necessarily stable or may have heavy magnitude overshoots, especially when the desired group delay is low. To overcome this shortcoming, a stability constraint that is characterized by the maximum pole radius is also imposed on the filters in this paper, resulting in IIR maximally flat stable digital filters (MFSDFs). An algorithm is presented for the design of the flatness and pole-radius constrained IIR filters with specified group delay. Using the proposed method, low-pass, high-pass, band-pass and band-stop IIR MFSDFs with low group delay have been designed. Results demonstrate the effectiveness of the proposed method and the superior performance of the IIR MFSDFs over existing MFDFs.
最大平坦数字滤波器（MFDFs）广泛应用于有用信号能量集中在某些特定频率附近的应用中。MFDFs的一种典型设计方法是在某些频率上对滤波器的频率响应及其一阶到高阶导数施加约束，并根据这些约束完全确定滤波器系数。然而，用这种方法设计的无限脉冲响应（IIR）MFDFs不一定稳定，或者可能有严重的幅度过冲，特别是当期望的群延迟较低时。为克服这一缺点，本文还对滤波器施加了以最大极点半径为特征的稳定性约束，从而得到IIR最大平坦稳定数字滤波器（MFSDFs）。提出了一种设计具有指定群延迟的平坦度和极点半径受限IIR滤波器的算法。使用所提出的方法，设计了具有低群延迟的低通、高通、带通和带阻IIR MFSDFs。结果证明了所提方法的有效性以及IIR MFSDFs相对于现有MFDFs的优越性能。
