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This paper proposes an algorithm to obtain the sampling factors to model any frequency partitioning so that it is realized using low complexity rational decimated non-uniform filter banks (RDNUFBs). The proposed algorithm is employed to approximate the Bark scale to find a rational frequency partitioning that can be realized using RDNUFBs with less approximation error. The proposed Bark frequency partitioning is found to reduce the average deviation in center frequency and bandwidth by 65.04% and 48.50% respectively, and root mean square bandwidth deviation by 54.46 % when compared to those of the existing perceptual wavelet approximation of Bark scale. In the first filter bank design approach discussed in the paper, a near perfect reconstruction partially cosine modulated filter bank is employed to obtain the improved Bark frequency partitioning. In the second design approach, the hardware complexity of the PCM based RDNUFB is reduced by deriving the channels with different sampling factors from the same prototype filter by the method of channel merging. There is a considerable reduction of 40.83 % in the number of multipliers when merging of partially cosine modulated channels is employed. It is also found that both the proposed approaches can reduce the delay by 95.17 % when compared to the existing rational tree approximation methods and hence, are suitable for real time applications.

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