What is it about?

A filter with delay-induced negative group delay is presented. The filter consists of multiple time-delayed feedback terms, which lead to a negative group delay for frequencies in the baseband. It can be used for the real-time prediction of band-limited signals. The filter is universal as 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 predicts the signal in real time up to a prediction horizon that depends on the cutoff frequency. How signal prediction arises from the negative group delay of the filter is worked out in detail. Its properties, including stability, are derived analytically and demonstrated by numerical simulations. For chaotic systems, the filter is predictive during phases of high predictability.

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Why is it important?

This predictor is universal in the sense that it's coefficients do not need to be adapted to the time series to be predicted.

Perspectives

There is an implementation of the filter in Matlab available, but it is so simple that it can be easily translated into any other programming language such as Python, Java, Kotlin.

Dr Henning U Voss
Weill Cornell Medicine

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This page is a summary of: A delayed-feedback filter with negative group delay, Chaos An Interdisciplinary Journal of Nonlinear Science, November 2018, American Institute of Physics, DOI: 10.1063/1.5052497.
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