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Further NFFT papers

Several papers have described fast approximations for the NFFT. Common names for NFFT are non-uniform fast Fourier transform [8], generalized fast Fourier transform [5], unequally-spaced fast Fourier transform [2], fast approximate Fourier transforms for irregularly spaced data [23], non-equispaced fast Fourier transform [10] or gridding [21,15,19].

In various papers, different window functions were considered, e.g. Gaussian pulse tapered with a Hanning window in [4], Gaussian kernels combined with sinc kernels in [19], and special optimised windows in [15,4]. Furthermore, special approaches based on scaling vectors [17], based on minimising the Frobenius norm of certain error matrices [18] or based on min-max interpolation [8] are proposed. However, the numerical results in [18,8] show that these approaches are not superior to the approach based on Kaiser-Bessel functions.

An even more general FFT, where both the knots in frequency and time/spatial domain are arbitrary, was developed in [6]. Up to now, the library does not support this extension.

Our algorithms are based on the approach in [20]. Here, one can change the window functions in a very simple way. See Section 3 and Section 4 for a suitable choice of the window function with respect to accuracy, speed and memory usage.


next up previous
Next: Inverse NFFT Up: Window functions Previous: Window functions
Stefan Kunis 2004-09-03