Studies on Circulator-Tree Wave Digital Filters

Abstract: A wave digital filter is derived from an analog filter, which is realized as classical doubly resistively terminated reactancefilters. Perfectly designed wave digital filters express good dynamic signal range, low roundoff noise and excellent stabilitycharacteristics with respect to nonlinearity which are produced due to finite wordlength effects. Wave digital filters inheritthe sensitivity properties from analog filters, therefore, coefficients values can be selected to favorable values.Wave digital filters, derived from ladder filters, have low coefficient sensitivity in the passband and stopband. These WDFsare very complicated and are non-modular. The lattice wave digital filters are modular and are not complex. However, theyhave very high sensitivity in the stopband and thus require large coefficient wordlengths. The number of coefficients equalsthe filter order which have to be odd.This thesis discusses the wave digital filter structures that are modular because they are designed by cascading the first-orderand second-order sections. These WDFs can be pipelined. They also exhibit all the above mentioned favorable properties.Similar to lattice WDFs, these structures are restricted to symmetrical and antisymmetrical transfer functions. The synthesisof these structures is based on the factorization of the scattering matrix of lossless two-ports.In this thesis work, lowpass wave digital filters based on circulator-tree structure are designed with different orders startingfrom 3 and going upto 13. In parallel to these circulator-tree wave digital filters, the simple digital filters are also designedwith the same specification. The results of the two filters are compared with each other. It is observed that impulse responseand attenuation response of the two kind of filters perfectly match. Therefore, it is can be concluded that circulator-tree WDFupto Nth order can be synthesized. The implementation examples of two filter with order 3 and order 7 is presented in thisdocumentation for ready reference. It has also been shown that the order of sections does not affect the transfer function ofthe filter. Noise has been introduced and adaptor sections are penetrated. From the results it is concluded that the order of theadaptor sections does not matter and also that the noise does not affect the other adaptors sections, it only propagates throughother adaptors sections.