FIR Adaptive filters based on hirschman optimal transform

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 transformbased 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 N , where N 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.

Hirschman Optimal Transform (HOT) DFT Block LMS Algorithm

“…In the HOT DFT block LMS algorithm, the fast HOT convolution is used to calculate the filter output and update the weights. Recently, the HOT transform was used to develop the HOT LMS algorithm (Alkhouli et al, 2005;, which is a transform domain LMS algorithm, and the HOT block LMS algorithm , which is a fast block LMS algorithm. The HOT DFT block LMS algorithm presented here is different from the HOT block LMS algorithm presented in .…”