A novel approach to design of signal matched QMF and DFT filter bank

Abstract

In this paper, we propose three different filter bank structures matched to a signals or its statistics namely: 2-channel uniform filter bank, M-channel dyadic nonuniform filter bank and M-channel modified DFT filter bank. First, 2-channel QMF analysis filter bank matched to a signal or its statistics is obtained. In order to obtain this filter bank, the given sequence is first divided into even and odd subsequences. For each subsequence predictor is estimated. By combining these predictors in such a way that the resultant signals represent the different frequency bands, analysis low pass and high pass filters are obtained and then by combining the inverses of linear predictors corresponding synthesis filters are easily obtained. In this manner two channel signal matched QMF bank is estimated by using same approach, we present, M-channel NUFB model matched to the signal or its statistics. To estimate the filters of this model, first we estimate two channel QMF analysis bank and then using the signal across the low pass subband, 2-channel analysis bank is obtained again in the same fashion. By cascading these two 2-channel analysis banks, 3-channel non-uniform filter with decimation factors {2 ,4, 4} matched to signal or its statistics is estimated. Further, proposed approach is also extended to find M-channel residual error DFT filter bank (modified DFT filter bank). In this approach, first given sequence is divided into M-subsequences and for each subsequence predictor coefficients are estimated and then these predictors are combine using DFT matrix. Filter banks design using proposed approach are computationally inexpensive and also they give compression results equal to or better than uniform counter part. To validate the theory the results of compression on speech clips are tabulated in the table.