Selective enhancement of space-time broadband spiral-waves using 2D IIR digital filters

Broadband space-time spiral-waves have received much attention in bioelectromagnetics and chaotic systems. They occur as propagating waves in non-linear active-media, such as the surface of the heart. A novel first-order 2D IIR practical-BIBO stable non-separable digital filter, based on a 2D signal derived from a circular-array of sampled sensors, is proposed for the real-time broadband highly-selective enhancement of broadband Archimedean spiral-waves and circular-waves in the presence of undesired spiral-waves. The proposed filter employs the spatio-temporal helix-transform, which is a form-preserving transform that converts a noncomputable 2D difference-equation into an equivalent 1D difference-equation. This transformation converts a noncomputable 2D IIR digital filter into a computable, and practically useful, 1D IIR approximate equivalent filter. The selective enhancement of broadband Gaussian spiral-wave and circular-waves are demonstrated where the desired spiral-waves are shown to be enhanced by approximately 22 dB. The computational complexity of the proposed filter is low, employing 3 multiplications and 6 additions/subtractions per output sample.