High-performance sparse fast Fourier transforms

Abstract

The sparse fast Fourier transform (SFFT) is a recent novel algorithm to compute discrete Fourier transforms on signals with a sparse frequency domain with an improved asymptotic runtime. Reference implementations exist for different variants of the algorithm and were already shown to be faster than state-of-the-art FFT implementations in cases of sufficient sparsity. However, to date the SFFT has not been carefully optimized for modern processors. In this paper, we first analyze the performance of the existing SFFT implementations and discuss possible improvements. Then we present an optimized implementation. We achieve a speedup of 2-5 compared to the existing code and an efficiency that is competitive to highperformance FFT libraries.

An Improved FPGA Implementation of Sparse Fast Fourier Transform

“…As can be seen from the figures, the advantage of the SFFT in computational complexity becomes more evident when the data length is increased to a moderate level, and compared with the recent SFFT implementation approaches in [4] and [9], the improved architecture still consumes less time and hardware resources.…”

Sparse Discrete Fractional Fourier Transform and Its Applications

“…As is pointed out in [21], the computational complexity of these two versions closely correlates with the signal size . The version 3 and 4 codes are not published yet.…”

“…This process is conducted by modifying the time-domain signal as we do not have access to the input signal's Fourier spectrum, which would require performing a DFT [21]. We permutate the constructed signal as follows:…”

“…Step 3) To extract parts of a signal in a smooth way and avoid spectral leakage, a window function is used [21]. Define a flat window function , which is a symmetric vector, .…”

“…The version 3 and 4 codes are not published yet. However, the theories of these two versions have been described in [29], and some analysis of version 3 can be found in [21]. It is proved that, in code version 3, the correlation between signal size and computational complexity becomes less significant.…”