An efficient transform decomposition method for sparse input points DFT in multiple-carriers cognitive radio system

Fast Fourier transform (FFT) is widely used in signal processing and communications such as digital filtering, spectral analysis, and multicarrier cognitive radio systems based on OFDM (orthogonal frequency-division multiplexing) and FBMC (filter-bank multi-carriers). There are several methods that have been developed to eliminate or reduce the computation within a DFT if the input points have many zeros or the number of output points acquired is relatively small, for example, transform decomposition (TD). TD can be seen as a modified Cooley-Tukey FFT where the DFT is decomposed into two smaller DFTs. In this paper, we propose a computationally efficient method for sparse input points DFT based on TD approach. The numerical analysis results show that the proposed method is more efficient than the conventional TD.