Hirschman Optimal Transform Block LMS Adaptive Filter

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 (1957). We use the result to develop a fast block-LMS adaptive filter which we call the HOT block-LMS adaptive filter. This filter requires slightly less than half of the computations that are required for the FFT block-LMS adaptive filter. The simulations show that the convergence rates of both the HOT and FFT block-LMS adaptive filters are similar.