The decomposition of large problems using single-sided subbanding

In this paper, we show that an NPR M-channel filter bank with a diagonal system inserted between the analysis and synthesis filterbanks, with appropriately chosen analysis and synthesis filters, may be used to decompose an arbitrary FIR system of O(L) into M FIR complex subband components each of O(L/K), where K is the downsampling rate. This decomposition is at the expense of using complex arithmetic for the subband processing. The proposed filter bank structure has application in the identification and equalization of long channels, (such as those that occur in reverberative environments) where existing algorithms may be intractable. By reducing the order of the problem in the subbands, such problems become computationally feasible. The improved performance and reduced computational requirements afforded by the proposed method are verified using the acoustic echo cancellation (AEC) problem as an example