Design and realization methods for IIR multiple notch filters and high-speed narrow-band and wide-band filters

Abstract

In this thesis, a direct IIR design method for real WDFs based on Gazsi's work is summarized in detail, and the cascade realization of first- and second-order allpass sections is generalized to any IIR transfer function, then a simple design method for bireciprocal lattice WDFs is given. A design and realization method for IIR multiple notch filters based on the phase of an allpass filter approximation is described. A design and realization method for high speed narrow-band and wide-band WDFs based on the IFIR technique is given, both nonlinear and approximately linear phase filters are considered; the narrow-band filter is composed of a model filter and one or several masking filters in cascade. In the case of nonlinear phase, conventional lattice and bireciprocal lattice WDFs are used for the model and masking filters; the overall narrow-band filters can be designed by separately designing the model and masking filters. The wide-band filter is composed of a narrow-band filter in parallel with a series of allpass filters, to obtain an overall wide-band filter. The narrow-band filter is designed first, and is then connected in parallel with one of the allpass filters of the narrow-band filter. In the case of approximately linear phase, the linear phase IIR filter is used for the model filter, and a maximum flat linear phase FIR filter is used for the masking filter. Several advantages of these filters over directly designed filters are that they have a substantially higher maximal sample frequency, lower roundoff noise and lower finite wordlength. Several design examples are given to demonstrate the properties of these filters.