The complex subband decomposition and its application to the decimation of large adaptive filtering problems

Submitted to IEEE Transactions on Signal Processing, Vol. 50, No. 11, pp. 2730-2743.
James P. Reilly, Matt Wilbur, Michael Seibert and Nima Ahmadvand

Abstract   In this paper, we show that an NPR M-channel filter bank with a diagonal system inserted between the analysis and synthesis filter banks may be used to decompose an FIR system of order L into M complex subband components each of order L/K , where K is the downsampling rate. This decomposition is at the expense of using complex arithmetic for the subband processing. The theory surrounding the proposed filter bank structure leads to a new understanding of subbanded adaptive filtering implementations. It also leads naturally to a delayless subbanded adaptive filter scheme.

Using conditions on the analysis and synthesis filters, the formulas for the subband components and their respective properties are developed. Simulation results for an acoustic echo cancellation example are given to support the developed theory.