A filter circuit includes a first stage comprising a first infinite impulse response (IIR) filter; a third stage comprising a third IIR filter; and a second stage interposed between the first stage and the third stage, the second stage comprising a second IIR filter, where an output terminal of the first IIR filter is coupled to an input terminal of the second IIR filter, and an output terminal of the second IIR filter is coupled to an input terminal of the third IIR filter, where the second stage of the filter circuit is configured to operate in an acquisition mode when a transient is detected in an input signal to the first IIR filter, where during the acquisition mode, the second stage of the filter circuit is bypassed.

An adaptive identification system, for identifying a propagation system characteristic by an adaptive filter, includes a signal generator that generates an identification input signal including a frequency component of an integer multiple of a fundamental frequency and having a periodicity satisfying a PE condition, a setting unit that sets moving average time to a fundamental period of the identification input signal, and an adaptive algorithm execution unit that uses a moving average value and a diagonal matrix to update a coefficient of the adaptive filter, the moving average value being obtained by calculating a moving average of a cross-correlation vector of a vector of the identification input signal and an observation signal with the moving average time, and the diagonal matrix being obtained by diagonalizing a matrix obtained by calculating a moving average of an autocorrelation matrix of the vector of the identification input signal with the moving average time.

A filter circuit includes a first stage comprising a first infinite impulse response (IIR) filter; a third stage comprising a third IIR filter; and a second stage interposed between the first stage and the third stage, the second stage comprising a second IIR filter, where an output terminal of the first IIR filter is coupled to an input terminal of the second IIR filter, and an output terminal of the second IIR filter is coupled to an input terminal of the third IIR filter, where the second stage of the filter circuit is configured to operate in an acquisition mode when a transient is detected in an input signal to the first IIR filter, where during the acquisition mode, the second stage of the filter circuit is bypassed.

An adaptive identification system, for identifying a propagation system characteristic by an adaptive filter, includes a signal generator that generates an identification input signal including a frequency component of an integer multiple of a fundamental frequency and having a periodicity satisfying a PE condition, a setting unit that sets moving average time to a fundamental period of the identification input signal, and an adaptive algorithm execution unit that uses a moving average value and a diagonal matrix to update a coefficient of the adaptive filter, the moving average value being obtained by calculating a moving average of a cross-correlation vector of a vector of the identification input signal and an observation signal with the moving average time, and the diagonal matrix being obtained by diagonalizing a matrix obtained by calculating a moving average of an autocorrelation matrix of the vector of the identification input signal with the moving average time.