Synthesis of discrete bandpass and notch filters using invariant impulse and transient characteristics

Abstract

The problem of constructing discrete bandpass and notch filters using impulse and transient characteristics of continuous analog filters of low and high frequencies is considered. A technique for the synthesis of tunable bandpass and notch filters with a constant width of the amplitude-frequency characteristics, regardless of the filter tuning frequency, is developed. The weight coefficients of the difference equations that determine the operation of discrete bandpass and notch filters with a constant width of the amplitude-frequency characteristics under conditions of a variable filter tuning frequency are found. The synthesis is based on the presentation of the mathematical frequency transfer function of the filter separately in the region of positive and negative frequencies, for each of which a bilinear z-transform is applied shifted to the tuning frequency of the selected region. The transfer functions in the z-plane of discrete filters are obtained separately for the regions of positive and negative frequencies. By summing and multiplying the transfer functions, the final transfer functions in the z-plane for discrete band pass and notch filters are obtained. By passing from the z-parameter to the jω parameter, expressions are obtained for the frequency transfer functions of the synthesized bandpass and notch filters. The amplitude-frequency characteristics of the synthesized filters are evaluated, and their width is shown to remain constant when the filter tuning frequency is changed. The developed technique is reported to be of use in building adaptive systems and signal processing devices, such as signal detection and filtering systems, Doppler velocity meters, and moving target selection systems.