Abstract
By decreasing the decimation ratio to one less than the number of channels, a perfect-reconstruction quadrature mirror filter (QMF) system can be constructed with the following innovative features: (1) the band division, which in the past has been uniform, can be made nonuniform; (2) the equivalent delay, which has usually been as large as the order of the dividing filter, can now be reduced to a size equal to the decimation ratio minus 1; (3) the number of channels, which has been restricted to a power of 2, can now be arbitrary. In addition, the traditional method employs spectral decomposition, while the proposed method employs Euclidean division. Euclidean structure (the realization of Euclidean division on a network) and lattice structure are considered as methods of constructing a filter that does not produce an aliasing distortion for the finite word length.
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