Adaptive lowpass filters

We propose a design of first-order adaptive infinite impulse response (IIR) low-pass filters to find the passband-edge frequencies of low-pass signals: we first show that gradient algorithms cannot directly be applied because the mean square errors (MSE) of IIR low-pass filter outputs have no extremum. Then we introduce a weighting function to be multiplied with the transfer function so that MSE has an extremum. Structures to realize the proposed adaptive low-pass filters are shown. Simulations confirm the convergency of the proposed algorithms