High-performance sparse fast Fourier transforms

The Sparse Fast Fourier Transform is a recent algorithm developed by Hassanieh et al. at MIT for Discrete Fourier Transforms on signals with a sparse frequency domain. A reference implementation of the algorithm exists and proves that the Sparse Fast Fourier Transform can be faster than modern FFT libraries. However, the reference implementation does not take advantage of modern hardware features like vector instruction sets or multithreading. In this Master Thesis the reference implementation’s performance will be analyzed and evaluated. Several optimizations are proposed and implemented in a high-performance Sparse Fast Fourier Transform library. The optimized code is evaluated for performance and compared to the reference implementation as well as the FFTW library. The main result is that, depending on the input parameters, the optimized Sparse Fast Fourier Transform library is two to five times faster than the reference implementation.

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