April 2008
Intermediate
832 pages
26h 2m
English
Content preview from Adaptive Filters
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CHAPTER 28 Block and Subband Adaptive Filters
Now that we know how to implement a long FIR filter (i.e., a long fullband convolution) efficiently by means of block processing, we can proceed to show how this result can be used to develop efficient block adaptive filters.
28.1 DFT BLOCK ADAPTIVE FILTERS
Thus, refer to the block implementation of Fig. 27.8. In a manner similar to (27.5), we define the vectors
We further let lk denote the M/B × 1 weight vector associated with Lk(z), and introduce the corresponding 
regression vector
Then the output of each Lk(z) is given by the inner product 
With this notation, we can express dB,n in terms of the subband filter coefficients {lk} as follows. Collect the regressors 
into a block diagonal matrix
(28.1) 
and the corresponding filter coefficients ...
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