Design of Wave Digital Filters with the TU Delft Toolbox

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.