A fast DFT method for generally k sparse signals recovery

In this paper, a new method to fast compute DFT of generally sparse signals is presented. Firstly, the original signal is downsampled with different time shifts, and the discrete Fourier Transforms (DFTs) of downsampled signals are calculated by FFT. Then the DFTs are used to determine and measure the K non-zero (significant) freq. grids by combining the moment preserving problem with the BigBand method. The proposed method is hardware-friendly, and simulation results show that the proposed method has better recovery performance compared with other methods.