Expansion of Sign Algorithm and Sensitivity Analysis for Adaptive Bandpass Filters With Tunable Center-Frequency

An adaptive state-space bandpass filter with tunable center-frequency is explored by combining the sign algorithm with the gradient-descent method appropriately. This enables one to attain much faster convergence of center-frequency than the existing method and reach the area near goal faster than directly applying the sign algorithm. Moreover, the $l_{2}-$sensitivities for state-space bandpass filters with tunable center-frequency are analyzed. An $l_{2}-$sensitivity measure is then derived to evaluate the whole $l_{2}-$sensitivities for the state-space bandpass filters with tunable center-frequency. Finally, a numerical example is presented to demonstrate the validity and effectiveness of the proposed adaptive iterative algorithm and $l_{2}-$sensitivity analysis.