Lattice Wave Digital Filters (LWDF) are a special class of IIR filters. They can be used to design lowpass, highpass, bandpass and bandstop filters, respectively. They comprise two allpass filters in parallel, where the advantages are twofold. Firstly, the implementation costs are lower than traditional filter designs, since they comprise less multipliers. Secondly, one can switch by a simple sign change from low- to highpass respectively bandpass to -stop filters. Traditional LWDF design techniques however show non-constant group delays in the passband, making them prohibitive in many applications.
The novel design technique however developed in this project and implemented in the attached MATLAB Toolbox offers nearly linear phase filters, employing optionally a collocation and a Ritz-Galerkin design method, where the collocation method is the default approach.
Moreover, the novel technique is capable to design half-band filters with extremely low effort, exploiting symmetries of half-band LWDF filters. Results of the magnitude response and group delay are shown in the figures.