Exponential Hyperbolic Cosine Robust Adaptive Filters for Audio Signal Processing

In recent years, correntropy-based algorithms which include maximum correntropy criterion (MCC), generalized MCC (GMCC), kernel MCC (KMCC) and hyperbolic cosine function-based algorithms such as hyperbolic cosine adaptive filter (HCAF), logarithmic HCAF (LHCAF), least lncosh (Llncosh) have been widely utilized in adaptive filtering due to their robustness towards non-Gaussian/impulsive background noises. However, the performance of such algorithms suffers from high steady-state misalignment. To minimize the steady-state misalignment along with having comparable computational complexity, an exponential hyperbolic cosine function (EHCF) based new robust norm is introduced and a corresponding EHCF based adaptive filter called exponential hyperbolic cosine adaptive filter (EHCAF) is developed in this letter. Further, computational complexity and bound on learning rate for stability of the proposed algorithm is also studied. A set of simulation studies has been carried out for system identification scenario to assess the performance of the proposed algorithm. Further, EHCAF algorithm has been extended and the filtered-x EHCAF (Fx-EHCAF) algorithm is proposed for robust room equalization.