Fast Fourier Aliasing-based Sparse Transform (FFAST) for calculating the Discrete Time Fourier (DFT) transform signals having sparse spectrum.

The distribution contains C++ source code for the FFAST engine, demo files and MATLAB scripts that interact with the tool.

The algorithm cleverly induces sparse graph alias codes in the DFT domain, by sub-sampling of the time-domain samples. The resulting sparse graph alias codes are then exploited in a peeling decoder.

Besides the noiseless and exactly sparse spectrum, the algorithm can handle the noisy setting. The algorithm is also observed to perform well in the case of off-grid spectra; however, theoretical guarantees are not given for that case.

• Display help

    ./ffast --help
  

• Run an FFAST experiment (-a) on randomly generated signals of length 124950 (-n 124950) having 10 sparse spectrum (-k 10) 30 times (-i 30)

    ./ffast -a -n 124950 -k 10 -i 30
  

• Run FFAST on input data saved in inFile.txt (-f inFile.txt)

    ./ffast -f inFile.txt
  

1. Computing a k-sparse n-length Discrete Fourier Transform using at most 4k samples and O(k logk) complexity -- S. Pawar and K. Ramchandran
2. A robust FFAST framework for computing a k-sparse n-length DFT in O(k log n) sample complexity using sparse-graph codes -- S. Pawar and K. Ramchandran
3. Robustifying the Sparse Walsh-Hadamard Transform without Increasing the Sample Complexity of O(K log N) -- X. Li, J.K. Bradley, S. Pawar, K. Ramchandran

Quentin Byron, Thibault Derousseaux, Rohan Varma, Xiao (Simon) Li, Orhan Ocal