SSP'05 -- Proceedings

	IEEE/SP 13th workshop on Statistical Signal Processing July, 17-20, 2005 - Bordeaux - France

Information regarding the paper

Title

FIR Adaptive Filters Based on the Hirschman Optimal Transform

Author(s)

Osama Alkhouli	University of Okalhoma
Victor DeBrunner	University of Okalhoma
Yan Zhai	University of Okalhoma
Mark Yeary	University of Okalhoma

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Abstract

In this paper, we derive a convolution theorem suitable for the Hirschman optimal transform (HOT), a unitary transform derived from a discrete-time, discrete-frequency version of the entropy-based uncertainty measure first described by Hirschman. We use the result to develop transform domain adaptive filters. First, we show how our method can be used to implement a fast block-LMS adaptive filter that we call the HOT block-LMS adaptive filter. This filter requires slightly less than half of the computations that are required in an FFT-based block-LMS adaptive filter. We also develop another transform-based adaptive filter algorithm that uses a sliding window instead of a block of data. The HOT version of these sliding algorithms is also significantly computationally more efficient (by , where is the filter order) than the sliding DFT version. Because our work is at an early stage, we develop simulations that explore basic convergence characteristics.