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Dr. Toni Volkmer
Software

sparseFFTr1l

sparseFFTr1l is a software library written in MATLAB for computing the sparse fast Fourier transform based on reconstructing rank-1 lattices in a dimension incremental way.

For further details, please read
  • Potts, D., Volkmer, T.
    Sparse high-dimensional FFT based on rank-1 lattice sampling.
    Appl. Comput. Harm. Anal. 41, 713 – 748, 2016. (pdf, DOI).

Download

sparseFFTr1l-0.1.5.tar.gz is the updated version of the library with bugfixes and Octave support.

prony_sparseFFT_iterative

prony_sparseFFT_iterative is a software library written in MATLAB for computing the sparse fast Fourier transform in an iterative way based on Prony's method via MUSIC or ESPRIT. There exists a one-dimensional version as well as a multi-dimensional version based on rank-1 lattice techniques.

For further details, please read
  • Potts, D., Tasche, M., Volkmer, T.
    Efficient spectral estimation by MUSIC and ESPRIT with application to sparse FFT.
    Front. Appl. Math. Stat. 2, 2016. (pdf, DOI).

Download

prony_sparseFFT_iterative-0.1.0.tar.gz is the first version of the library.

nonperiodicR1L

nonperiodicR1L is a software library written in MATLAB for computing Chebyshev coefficients based on samples along reconstructing rank-1 Chebyshev lattices.

For further details, please read
  • Potts, D., Volkmer, T.
    Fast and exact reconstruction of arbitrary multivariate algebraic polynomials in Chebyshev form.
    Proceedings of the 11th International Conference on Sampling Theory and Applications, 392–396, 2015. (pdf, DOI).
  • Potts, D., Volkmer, T.
    Sparse high-dimensional FFT based on rank-1 lattice sampling.
    Appl. Comput. Harm. Anal. 41, 713 – 748, 2016. (pdf, DOI).

Download

nonperiodicR1L-0.1.1.tar.gz is the updated version of the library with minor bugfixes.

taylorR1Lnfft

taylorR1Lnfft is a software library written in MATLAB for computing approximated Fourier coefficients based on samples along perturbed nodes of reconstructing rank-1 lattices.

For further details, please read
  • Volkmer, T.
    Taylor and rank-1 lattice based nonequispaced fast Fourier transform.
    In 10th international conference on Sampling Theory and Applications (SampTA 2013), pages 576–579, Bremen, Germany, July 2013. (pdf).
  • Kämmerer, L., Potts, D., Volkmer, T.
    Approximation of multivariate periodic functions by trigonometric polynomials based on rank-1 lattice sampling.
    J. Complexity 31, 543–576, 2015. (pdf).

Download

taylorR1Lnfft-0.1.1.tar.gz is the updated version of the library with minor bugfixes.