Design and implementation of linear phase wave digital filters

Abstract

A steady increase of research within the field of digital systems has resulted ip a wide acceptance of the discrete approach to system design. Research has produced discrete techniques that complement those already in use in the analogue domain. A rapid improvement in the performance and availability of digital hardware has prompted a move from analogue to digital systems, especially within the field of signal processing. This thesis considers the design of Wave Digital Filters (WDF's) to satisfy arbitrary magnitude and phase specifications with finite word length coefficients. It describes the structures and properties of ladder and lattice WDF's related to linear phase design through coefficient sensitivity and non-minimum-phase. The initial part of this thesis concentrates upon the design and comparison of optimization techniques to satisfy magnitude-only and simultaneous low-pass frequency specifications upon ladder and lattice WDF's. Experiments confirm the unsuitability of the ladder WDF for simultaneous designs because of their minimum-phase characteristics. Successful simultaneous low pass designs upon lattice WDF's were achieved through quasi-Newton algorithms using a dual line template scheme and a weighted Lp-metric error function. The All Pass Sections(APS's) used to construct the low pass lattice WDF were investigated and a range of APS's considered that would allow the lattice WDF structure to satisfy high pass, single band pass and dual band pass frequency specifications. Special case APS's for single and dual band pass designs were generated by applying frequency transformations to the 1st and 2nd order low pass APS's. Equations and characteristics for these APS's are detailed along with a number of examples of filter deigns. The final area of this thesis concerns the design of finite word length solutions to magnitude-only and simultaneous frequency specifications, ranging from low pass to dual band pass type responses. Using the large word length solutions generated through the quasi-Newton optimization techniques as starting coefficients, a Hookc-Jceves direct search algorithm was implemented to generate finite word length solutions. Techniques detailed in this thesis provide a method for the generation of finite word length coefficients that satisfy arbitrary magnitude-only and simultaneous frequency specifications through optimization for the lattice WDF's