Comparison of Transform Domain Adaptive Filters, with Emphasis on the Hartley Transform

摘要

The least mean square (MLS) algorithm is the most often used real-time adaptive filtering algorithm due to its computational simplicity and remarkably good fit to the optimal Wiener solution. There have been many transform domain algorithms proposed for improving the convergence rate of the LMS algorithm, the most popular of which had been the Discrete Fourier Transform (DFT). However, the DFT requires complex arithmetic and thus, has proven computationally undesirable for applications involving only real signals. A number of unitary, real transforms have been proposed as less costly replacements for the DFT. These include the Discrete Cosine Transform (DCT), the Discrete Walsh Hadamard Transform (WHT), and the Power of Two Transform (PO2). Each of these in some vary exhibits a property necessary to speed the convergence rate, at a lower computational cost than the DFT. The work investigates the use of another real transform, the Discrete Hartley transform (DHT), for adaptive system estimation and adaptive echo cancelling. It is shown that the DHT performs better than these other real transforms under most circumstances. Its relationship to the DFT is such that it can be transformed into the DFT with simple algebraic manipulation. Keywords: Adaptive filters; Orthogonal transforms.