S. Douglas. Efficient approximate implementations of the fast affine projection using orthogonal transforms. In Proceedings of IEEE Int. Conf. Acoust., Speech, Sig. Proc.,  Home/Search   Document Details and Download   Summary   Related Articles   Check

....methods are effective rank reducing mechanisms which use the singular value decomposition (SVD) of the data matrix, given by X = USV H [7] or its eigen value decomposition (EVD) The Discrete Cosine Transform (DCT) has been proved to be asymptotically close to an eigen decomposition. Douglas [3] uses this property to find the approximate inverse of the correlation matrix that occurs in the affine projection algorithm. Our transform domain adaptive filtering framework, as introduced in [9] is based on the linear least squares problem. Let XM ThetaN = x 1 ; x 2 ; xN ] be the ....

S. Douglas. Efficient approximate implementations of the fast affine projection using orthogonal transforms. In Proceedings of IEEE Int. Conf. Acoust., Speech, Sig. Proc.,

....[26] or the EVD of the associated correlation matrix. Sometimes, data independent transforms are used as an approximation to the data dependent SVD and EVD. For example, Douglas uses the DCT [27] to find the approximate inverse of the correlation matrix that occurs in affine projection [28]. Our method has some similarities with a subband approach without decimation and cross filtering. II. Low Rank Adaptive Filtering In this section, we first interpret time domain and transform domain methods into a matrix framework. We then introduce a new low rank adaptive filtering approach. ....

.... obtained through the affine projection algorithm of order 2 (AP(2) Extending this concept, if Q 1 = I N ThetaN , then this system considers the latest N equations, and the solution is equivalent to that obtained through the rectangularly windowed RLS solution (for N M ) Similarly, in [28], Q 1 = h Q DCT P ThetaP 0 P ThetaN GammaP i . October 20, 1999 DRAFT IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. XX, NO. Y, MONTH 1999 7 We have thus shown that NLMS and AP can be obtained from the overdetermined RLS case by using a low rank transformation. The question that now arises ....

S. Douglas, "Efficient approximate implementations of the fast affine projection using orthogonal transforms," in Proceedings of IEEE Int. Conf. Acoust., Speech, & Signal Proc.,

....h(k 1) h(k) XM ThetaN Gamma X T M ThetaN XM ThetaN Delta Gamma1 eN : 12) 2. TRANSFORM DOMAIN ADAPTIVE FILTERING Transform domain filtering involves a unitary transformation of the input data, and then using the transformed data as input to a normal adaptive filtering implementation [2, 4, 6]. Some of the most commonly used data independent transformations are DFT and DCT and the most commonly used data dependent transformation is SVD (or EVD) The advantages of transform domain adaptive filtering depend on exactly how transform domain filtering is implemented, but they can be either ....

....on these values. This part of our implementation is the dominant one in terms of complexity. For further fairness in comparison, we have included AP(4) although the implementation of our method is of rank 1. There is also a transform domain implementation of AP(4) denoted TAP(p) technique [2] included. In figure 3, we show tap weight error for the methods illustrated in figure 2. In figure 4, we show the actual filter response together with the ultimate filters obtained by three of the approaches illustrated in figure 3. 6. CONCLUSIONS We have presented a new, optimal approach to low ....

S. Douglas. Efficient approximate implementations of the fast affine projection algorithms using orthogonal transformations. In Proceedings of ICASSP96, pages 1656--1659, 1996.

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