Unsupervised FIR adaptive filtering and its frequency domain analysis

An unsupervised minimum mean square error FIR adaptive filtering(UAF) algorithm is proposed to estimate the system’s input signal.The algorithm only uses the system’s output signal and noise variance without requiring knowledge of a reference signal.The frequency analysis shows that the UAF is a multi-spot bandpass filter with passing frequency determined by the system’s input signal.Namely,the UAF chooses the expected frequency and extremely restricts the unwanted frequency signal by using weight-updating scheme in time domain.However,the UAF presents the Gibbs phenomenon since the ideal filter is infinitely long which is unrealizable.The simulation and experimental results show that the UAF could effectively reduce the amplitude of the noise and improve the signal to noise ratio.