Complex discrete comb filters with individually tunable partial domains

Problem Statement. The design of tunable complex discrete non-recursive and recursive bandpass and bandstop comb filters is currently a highly relevant task for solving problems of selecting useful signals against powerful correlated interference, creating various automatic systems, etc. Goal. Creation of low- and high-pass filters based on continuous-wave analogs. A method for synthesizing complex discrete comb bandpass and bandstop filters with individual tuning of individual partial frequency response regions has been developed. Results. Based on the invariant time and frequency responses of continuous low- and high-pass analog filters, weighting coefficients for difference equations were found that govern the operation of non-recursive and recursive complex discrete bandpass and bandstop comb filters with the ability to individually tune individual partial frequency response regions. The synthesis of non-recursive bandpass comb filters is based on the summation of the pulse and incremental transient responses of individual bandpass filters. To construct discrete recursive bandpass and bandstop comb filters, summation and multiplication of transfer functions in the z-plane were used. Weighting coefficients of difference equations of discrete bandpass and bandstop comb filters are obtained using the specified time and frequency responses of continuous low- and high-pass analog filters. A frequency-shifted bilinear z-transform is presented. Transfer functions of the synthesized discrete comb bandpass and bandstop filters are obtained. By summing the transfer functions for the bandpass filters and multiplying the transfer functions for the comb filters, the final transfer functions for the discrete bandpass and bandstop comb filters are obtained. The amplitude-frequency responses of the bandpass and bandstop comb filters are calculated. It is shown that the tuning frequency, width, and shape of the amplitude-frequency responses of individual partial regions of the comb filters can be individually and operationally changed. Practical significance. The developed method for synthesizing complex discrete bandpass and notch comb filters with individual tuning of individual partial frequency response regions will be highly useful in constructing adaptive systems and signal processing devices, such as signal detection and filtering systems, Doppler velocimeters, and moving target selection systems.