Adaptive Filters

Summary and Notes

The chapters in this part describe several adaptive structures that are meant to reduce the computational requirements of LMS and improve its convergence speed.

SUMMARY OF MAIN RESULTS

1. text describes three classes of efficient adaptive structures: transform-domain filters, block adaptive filters, and subband adaptive filters.
2. Transform-domain filters exploit the de-correlation properties of some unitary signal transforms, such as the discrete Fourier transform (DFT) and the discrete cosine transform (DCT), in order to pre-whiten the input data and speed up filter convergence. Designing a transform-domain filter usually involves three steps:
   1. (i) Replacing the regression vector u_i by a transformed version , where T is a unitary transformation.
   2. (ii) Employing a diagonal step-size matrix that consists of estimates of the inverse powers in the individual entries of .
   3. (iii) Making sure that the elements of the transformed regressor can be evaluated efficiently in O(M) operations.

      Steps (i)–(iii) only help improve the convergence speed of LMS; they do not result in a reduction of computational complexity. Two types of transformed filters were discussed in the text: DFT-LMS and DCT-LMS.

3. Block adaptive filters reduce the computational cost of LMS by some factor α > ...