Myriad-Type Polynomial Filtering

• Published in: IEEE transactions on signal processing Vol. 55; no. 2; pp. 747 - 753
• Main Authors: Aysal, T.C., Barner, K.E.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.02.2007; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: alpha -stable distributions; Applied sciences; Detection, estimation, filtering, equalization, prediction; Exact sciences and technology; Filtering; Filters; Filtration; Higher order statistics; impulsive processes; Information, signal and communications theory; Laplace equations; myriad filters; Nonlinear systems; polynomial filtering; Polynomials; Pulse width modulation; Robustness; Samples; Signal and communications theory; Signal processing; Signal, noise; Simulation; Statistical analysis; Statistical distributions; Statistical methods; Statistics; Telecommunications and information theory; Volterra series; Performance evaluation; Outlier; impulsive processes; stable distributions; Weighting filter; Filtering; Volterra series; Linear combination; Simulation; myriad filters; Higher order statistics; polynomial filtering
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2006.885758

Linear combinations of polynomial terms yield poor performance in environments characterized by heavy-tailed distributions. Weighted myriad (WMy) filters, however, are well known for their outlier suppression and detail preservation properties. It is shown here that the WMy methodology is naturally extended to the polynomial sample case, yielding filter structures that exploit the higher order statistics of the observed samples while simultaneously being robust to outliers for heavy-tailed distributions environments. Moreover, the introduced power weighted myriad (PWMy) filter class is well motivated by analysis of cross- and square-term statistics of heavy-tailed distributions. The effectiveness of the proposed filter is evaluated through simulations