Contents

• Introduction
• Notation, the NDFT, and the NFFT
  • NDFT - nonequispaced discrete Fourier transform
  • NFFT - nonequispaced fast Fourier transform
  • Available window functions and evaluation techniques
  • Further NFFT approaches
  
  
• Generalisations and inversion
  • NNFFT - nonequispaced in time and frequency fast Fourier transform
  • NFCT/NFST - nonequispaced fast (co)sine transform
  • NSFFT - nonequispaced sparse fast Fourier transform
  • FPT - fast polynomial transform
  • NFSFT - nonequispaced fast spherical Fourier transform
  • Solver - inverse transforms
  
  
• Library
  • Installation
  • Procedure for computing an NFFT
  • Generalisations and nomenclature
  • Inversion and solver module
  
  
• Examples
  • Computing your first transform
  • Computation time vs. problem size
  • Accuracy vs. window function and cut-off parameter $m$
  • Computing an inverse transform
  
  
• Applications
  • Summation of smooth and singular kernels
  • Fast Gauss transform
  • Summation of zonal functions on the sphere
  • Iterative reconstruction in magnetic resonance imaging
  • Computation of the polar FFT
  • Radon transform, computer tomography, and ridgelet transform
  
  
• Bibliography