A universal negative group delay filter for the prediction of band-limited signals

Abstract

A filter for universal real-time prediction of band-limited signals is presented. The filter consists of multiple time-delayed feedback terms in order to accomplish anticipatory coupling, which again leads to a negative group delay for frequencies in the baseband. The universality of the filter arises from its property that it does not rely on a specific model of the signal. Specifically, as long as the signal to be predicted is band-limited with a known cutoff frequency, the filter order, the only parameter of the filter, follows and the filter predicts the signal in real time up to a prediction horizon that depends on the cutoff frequency, too. It is worked out in detail how signal prediction arises from the negative group delay of the filter. Its properties, including stability, are investigated theoretically, by numerical simulations, and by application to a physiological signal. Possible control and signal processing applications of this filter are discussed.