One of the earliest works on transformdomain adaptive filtering was published in 1978 by Dentino et al. [4], in which the concept of adaptive filtering in the frequency domain was proposed. | W. Kenneth Jenkins et. Al. Transform Domain Adaptive Filtering. 2000 CRC Press LLC. http . Transform Domain Adaptive Filtering W. Kenneth Jenkins University of Illinois Urbana-Champaign Daniel F. Marshall MIT Lincoln Laboratory LMS Adaptive Filter Theory Orthogonalization and Power Normalization Convergence of the Transform Domain Adaptive Filter Discussion and Examples Quasi-Newton Adaptive Algorithms A Fast Quasi-Newton Algorithm Examples The 2-D Transform Domain Adaptive Filter Block-Based Adaptive Filters Comparison of the Constrained and Unconstrained Frequency Domain Block-LMS Adaptive Algorithms Examples and Discussion References One of the earliest works on transform domain adaptive filtering was published in 1978 by Dentino et al. 4 in which the concept of adaptive filtering in the frequency domain was proposed. Many publications have since appeared that further develop the theory and expand the current understanding of performance characteristics for this class of adaptive filters. In addition to the discrete Fourier transform DFT other orthogonal transforms such as the discrete cosine transform DCT and the Walsh Hadamard transform WHT can also be used effectively as a means to improve the LMS algorithm without adding too much computational complexity. For this reason the general term transform domain adaptive filtering is used in the following discussion to mean that the input signal is preprocessed by decomposing the input vector into orthogonal components which are in turn used as inputs to a parallel bank of simpler adaptive subfilters. With an orthogonal transformation the adaptation takes place in the transform domain as it is possible to show that the adjustable parameters are indeed related to an equivalent set of time domain filter coefficients by means of the same transformation that is used for the real time processing 5 14 17 . A direct form FIR digital filter structure is shown in Fig. .
