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Related Experiment Videos

Nonuniform fast Hankel transform (NUFHT) algorithm.

Q H Liu1, Z Q Zhang

  • 1Department of Electrical and Computer Engineering, Duke University, Durham, North Carolina 27708, USA. qhliu@ee.duke.edu

Applied Optics
|March 8, 2008
PubMed
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A new fast Hankel transform (FHT) algorithm computes Hankel transforms using nonuniformly spaced points. This method overcomes limitations of previous algorithms, offering greater accuracy and flexibility for diverse applications.

Area of Science:

  • Numerical analysis
  • Applied mathematics
  • Signal processing

Background:

  • Fast Hankel transform (FHT) algorithms traditionally require logarithmically spaced sample points.
  • This uniform spacing limits the applicability of FHT in various scientific and engineering fields.

Purpose of the Study:

  • To develop a fast Hankel transform algorithm capable of handling nonuniformly spaced sample points.
  • To overcome the limitations of existing FHT algorithms regarding sample point distribution.

Main Methods:

  • Utilized a novel nonuniform fast Fourier transform (FFT) algorithm.
  • Adapted the nonuniform FFT to compute Hankel transforms on arbitrary sample point distributions.

Main Results:

Related Experiment Videos

  • Achieved accurate computation of Hankel transforms for nonuniformly spaced data.
  • Demonstrated significantly higher accuracy compared to previous FHT algorithms.
  • Introduced enhanced flexibility for FHT applications.

    • Conclusions:

    • The developed nonuniform FHT algorithm effectively addresses the limitations of previous methods.
    • This advancement provides a more versatile tool for computations involving Hankel transforms.
    • The algorithm's flexibility opens new possibilities in signal processing and other domains.