A Novel Variational Digital Filtering Method

In this paper, a novel variational filtering processing method is proposed, which can realize lowpass/highpass filtering and bandpass/bandstop filtering of signals by constructing the corresponding variational minium problem with constrain and solving it by mean of the augmented Lagrangian and the alternate direction method of multipliers algorithm. The method presented eliminates the phase delay between output and input signal, while maintaining the low-distortion property of output signal. In the experiments, the variational filtering method is applied to simulated and actual signal to assess the validity of the approach. Results show that the proposed variational digital filtering method achieves low-distortion filtering. And compared with the commonly used zero-phase forward-backward Butterworth filter, the proposed method has a better filtering effect.