DFT algorithm based on FIR filter banks

A discrete Fourier transform (DFT) algorithm based on filter banks (FBs) for computation of an N-point DFT from M DFTs of length N/M is presented. The input signal of length N is analysed with an M-band finite impulse response (FIR) FB yielding M subband signals. These are aliased in the time-domain to produce M sequences of length N/M the DFTs of which are then adequately combined to yield the DFT of the input. A significant reduction in computational complexity results if the DFT of the input signal is estimated using some instead of all the M lower-length DFTs. In this case the proposed algorithm outperforms the subband DFT (SB-DFT) method with respect to estimation accuracy. More specifically, due to the highly frequency selective filters used to analyse the input data, the proposed method substantially reduces the aliasing encountered with SB-DFT, while due to the perfect reconstruction property of the FB employed, it yields the DFT samples with correct amplitude and phase in the band of interest. Experimental results highlight these points and support the analysis.