Design of Wave Digital Filters with the TU Delft Toolbox

Moritz Tockner, H. Brachtendorf, M. Steiger
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Abstract

This paper presents a method for the design of lattice wave digital filters (LWDFs) with an approximately linear phase response. A recently developed algorithm for the design of approximately linear phase allpass filters was utilized in combination with the LWDF structure, to synthesize frequency selective filters with a high phase response flatness. An iterative optimization method to generate such an LWDF for a given set of frequency response constraints was implemented and integrated into an open source LWDF design toolbox to allow an outreach to a broader audience. Additionally, the generated floating point LWDF coefficients can be quantized as multiplier-free signed digits by solving a nonlinear optimization problem. The design toolbox finds the coefficient representation requiring the minimum number of additions and/or subtractions, while still satisfying a given set of frequency response constraints. The results show the effectiveness of the filter design method compared to standard designs such as Butterworth, Tschebyscheff or Cauer and they highlight the differences to another existing linear phase method of the toolbox. A significant improvement can be seen in a comparison between the signed digit quantization compared to simple coefficient rounding.
用TU Delft工具箱设计波浪数字滤波器
本文提出了一种近似线性相位响应的点阵波数字滤波器的设计方法。结合LWDF结构,提出了一种设计近似线性相位全通滤波器的新算法,合成了相位响应平坦度高的频率选择滤波器。实现了一种迭代优化方法,用于为给定的一组频率响应约束生成这样的LWDF,并将其集成到开源LWDF设计工具箱中,以允许向更广泛的受众进行扩展。此外,通过求解非线性优化问题,可以将生成的浮点LWDF系数量化为无乘数的有符号数字。设计工具箱找到需要最少数量的加法和/或减法的系数表示,同时仍然满足给定的一组频率响应约束。结果表明,与Butterworth, Tschebyscheff或Cauer等标准设计相比,滤波器设计方法的有效性,并突出了与工具箱中另一种现有线性相位方法的差异。与简单的系数舍入相比,在有符号数字量化之间的比较中可以看到显著的改进。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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