Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

The extended Fourier transform for 2D spectral estimation.

G S Armstrong1, V A Mandelshtam

  • 1Chemistry Department, University of California-Irvine, Irvine, CA 92697-2025, USA. garmstro@uci.edu

Journal of Magnetic Resonance (San Diego, Calif. : 1997)
|November 9, 2001
PubMed
Summary
This summary is machine-generated.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Sensitivity analysis of solutions of the harmonic inversion problem: are all data points created equal?

Journal of magnetic resonance (San Diego, Calif. : 1997)·2010
Same author

Semiclassical spectra and diagonal matrix elements by harmonic inversion of cross-correlated periodic orbit sums.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics·2002
Same author

Pseudotime Schrödinger equation with absorbing potential for quantum scattering calculations.

Physical review letters·2001
Same author

The multidimensional filter diagonalization method.

Journal of magnetic resonance (San Diego, Calif. : 1997)·2000
Same author

The multidimensional filter diagonalization method.

Journal of magnetic resonance (San Diego, Calif. : 1997)·2000
Same author

Pure absorption electron spin echo envelope modulation spectra by using the filter-diagonalization method for harmonic inversion.

Journal of magnetic resonance (San Diego, Calif. : 1997)·1999

We introduce the eXtended Fourier Transform (XFT), a new spectral estimation method for truncated time signals. XFT combines discrete Fourier transform (DFT) with regularized resolvent transform (RRT) for enhanced resolution tuning.

Area of Science:

  • Signal Processing
  • Spectroscopy
  • Linear Algebra

Background:

  • Spectral estimation from truncated time signals is challenging.
  • Existing methods like the discrete Fourier transform (DFT) have limitations in resolution.
  • The regularized resolvent transform (RRT) offers potential for improved estimation.

Purpose of the Study:

  • To present a novel linear algebraic method, the eXtended Fourier Transform (XFT).
  • To enhance spectral estimation from truncated time signals.
  • To provide a tunable method for balancing spectral resolution and fidelity to the finite DFT.

Main Methods:

  • Developed XFT as a hybrid of DFT and RRT.
  • RRT is used to estimate the remainder of a finite DFT.
  • Regularization, controlled by parameter q, is applied to the ill-conditioned RRT problem.

Related Experiment Videos

  • Optimal q is selected based on data fit and signal-to-noise ratio.

    • Main Results:

    • XFT provides a method to "tune" spectral estimates.
    • The method allows adjustment between high-resolution estimates and the finite DFT.
    • Demonstrated both 1D and 2D XFT applications.
    • Successfully applied XFT to experimental Nuclear Magnetic Resonance (NMR) signals.

    Conclusions:

    • XFT offers a flexible and effective approach to spectral estimation.
    • The method addresses limitations of traditional spectral analysis techniques.
    • XFT shows promise for analyzing complex spectroscopic data, particularly in NMR.