Design of a negative group delay filter via reservoir computing approach: Real-time prediction of chaotic signals

An optimal arbitrary order filter with negative group delay is proposed for a real-time prediction of complex band-limited signals. The filter consists of a set of second-order linear dissipative oscillators and is determined by a rational transfer function with fixed poles and optimized zeros. The filter design and optimization algorithm is based on a reservoir computing approach. The predictive properties of the filter are demonstrated numerically for two chaotic model systems — the finite-dimensional Rössler system and the infinite-dimensional Mackey-Glass system, as well as for the real biological signal of the fingertip photoplethysmogram.