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

TL;DR

This paper introduces a universal real-time filter with negative group delay for predicting band-limited signals, independent of specific signal models, with applications demonstrated on physiological data.

Contribution

The paper presents a novel universal negative group delay filter that predicts band-limited signals in real time without relying on signal-specific models.

Findings

The filter achieves real-time prediction with a horizon depending on the cutoff frequency.

Theoretical and numerical analysis confirms filter stability and effectiveness.

Application to physiological signals demonstrates practical utility.

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.