Adaptive centre-frequency bandpass state-space digital filters and their <i>l</i> ₂ -sensitivity analysis

This paper explores an adaptive centre-frequency bandpass state-space digital filter by expanding a sign algorithm into the gradient-based method. To this end, a simple method for deriving a bandpass state-space digital filter with tuneable centre-frequency from a prototype low-pass filter and low-pass/bandpass transformation is presented. An adaptive iterative algorithm is then developed by expanding a sign algorithm into the gradient-based method. Also, $ l_2 $ -sensitivities for the bandpass state-space digital filter with tuneable centre-frequency are analysed where an $ l_2 $ -sensitivity measure for evaluating the whole $ l_2 $ -sensitivities is deduced. Numerical experiments are included to demonstrate the validity and effectiveness of the adaptive centre-frequency bandpass state-space digital filter and the $ l_2 $ -sensitivity analysis.