A DFT algorithm based on filter banks: the extended subband DFT

A DFT algorithm, the Extended Subband DFT (ESB−−DFT), is presented, which aims to overcome the problem of low accuracy the Subband DFT (SB−−DFT) algorithm suffers from, when applied in its approximate mode for signals with full spectrum. The proposed ESB−DFT is based upon the analysis of the input signal using a Filter Bank (FB) and the computation of its DFT from the lower length DFTs that correspond to the subband signals resulting from the analysis. The proposed 1D scheme is also extended to yield the 2D ESB−−DFT algorithm. The approximate mode of ESB−−DFT is then introduced with a detailed error analysis, which shows that it is possible to substantially reduce the computational complexity while obtaining a very accurate DFT estimate within a band of interest. The proposed ESB−−DFT is tested and compared to SB−−DFT for 1D and 2D signals. It is shown that ESB−−DFT substantially improves the estimation accuracy of SB−−DFT, while when applied in its full−−mode yields the exact DFT of the input.