On Minimal Second-order IIR Bandpass Filters with Constrained Poles and Zeros

In this paper, several forms of infinite impulse response (IIR) bandpass filters with constrained poles and zeros are presented and compared. The comparison includes the filter structure, the frequency ranges and a number of controlled parameters that affect computational efforts. Using the relationship between bandpass and notch filters, the two presented filters were originally developed for notch filters. This paper also proposes a second-order IIR bandpass filter structure that constrains poles and zeros and can be used as a minimal parameter adaptive digital second-order filter. The proposed filter has a wider frequency range and more flexibility in the range values of the adaptation parameters.

Suppression of correlated interference by adaptive notch filters under pulse repetition period modulation

Introduction: We discuss the problem of correlated noise suppression by adaptive complex notch filters of various orders. In order to eliminate the dependence of the transmission coefficient of the useful signal on its frequency, the pulse repetition period is modulated. Purpose: Studying the influence of pulse repetition period modulation on the correlated noise suppression coefficient. Methods: The notch filter parameters were optimized with the criterion of minimum average dispersion of correlated noise at the output of the filters during the repetition period modulation. Results: Expressions are obtained for the variance of correlated noise at the output of complex adaptive filters of various orders when the repetition period is modulated. Relationships are given for finding the optimal values ​​of the tuning frequency and coefficients of the notch filters which minimize the correlated noise level at their output. Expressions are obtained for the coefficients of correlated noise suppression by notch filters in the context of pulse repetition period modulation. The graphs are presented showing how the correlated noise suppression coefficient depends on the relative value of the probing signal repetition period deviation for various values ​​of the correlated noise spectral density width at optimal or non-optimal values ​​of the tuning frequency and coefficients of the notch filters. It is shown that the use of probing pulse repetition period modulation leads to a decrease in the correlated noise suppression coefficient. On the other hand, the adaptation of the weighting coefficients for the adopted models of notch filters and correlated interference provides an increase in the suppression coefficient. Practical relevance: When developing or studying correlated noise suppression systems, the obtained results make it possible, taking into account the permissible losses of the suppression coefficient, to reasonably choose the input pulse repetition period deviation value in order to eliminate the effect of “blind” frequencies.