Tutorials and application demos

The following are instructive demos of using FINUFFT for a variety of spectrally-related tasks arising in scientific computing and signal/image processing. We will slowly grow the list (contact us to add one). For conciseness of code, and ease of writing, they are in MATLAB (and should work on versions at least back to R2017a), unless otherwise stated.

• Fast evaluation of Fourier series at arbitrary points
  • 1D Fourier series
  • 2D Fourier series
• Efficient evaluation of (continuous) Fourier transforms
  • 1D FTs evaluated at arbitrary frequencies
  • Faster FTs when frequencies lie on a grid
  • 1D FTs of singular functions
  • 2D FTs
  • Further reading
• Periodic Poisson solve on non-Cartesian quadrature grid
• Periodic Poisson solve on non-Cartesian quadrature grid (Python)
• Efficient sampling from Gaussian Random Fields (GRFs)
  • Further reading
• Inverse 1D type 2 NUFFT: fitting a Fourier series to scattered samples
  • Well-conditioned example
  • Ill-conditioned example
  • Further reading

For further applications, see references, and:

• These software tutorial PDF slides.

• These seminar PDF slides.

• Fast Fresnel diffraction for optics and acoustics applications.

• Equispaced Fourier methods for Gaussian process regression as described in https://arxiv.org/abs/2210.10210 and https://arxiv.org/abs/2305.11065

• Tutorials for PyNUFFT with 1D and 2D reconstruction examples here.

• The numerical sampling of random plane waves.