On Performance of Sparse Fast Fourier Transform Algorithms Using the Aliasing Filter

Computing the sparse fast Fourier transform (sFFT) has emerged as a critical topic for long time because of its high efficiency and wide practicability. More than twenty different sFFT algorithms compute discrete (DFT) by their unique methods so far. In order to use them properly, urgent great concern is how analyze evaluate performance these in theory practice. This paper mainly discusses technology using aliasing filter. first part, introduces three frameworks: one-shot framework based on compressed sensing (CS) solver, peeling bipartite graph iterative binary tree search. Then, we obtain conclusion six corresponding algorithms: sFFT-DT1.0, sFFT-DT2.0, sFFT-DT3.0, FFAST, R-FFAST, DSFFT theory. second make two categories experiments computing signals SNRs, lengths, sparsities standard testing platform record run time, percentage signal sampled, L0, L1, L2 errors both exactly case general case. The results analyses are our guide optimize selectively.