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The Fast Fourier Transform (FFT) is a computational algorithm designed to compute the Discrete Fourier Transform (DFT) efficiently. By breaking down the calculations into smaller, manageable sections, the FFT significantly reduces the computational complexity involved. Direct computation of an N-point DFT requires N2 complex multiplications, whereas the FFT algorithm needs only (N/2)log⁡2N multiplications, offering a much faster performance.
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Signal processing techniques are essential for accurately converting continuous signals to digital formats and vice versa. When a continuous signal is sampled with a period T, the resulting sampled signal exhibits replicas of the original spectrum in the frequency domain, spaced at intervals equal to the sampling frequency. To handle this sampled signal, a zero-order hold method can be applied, which creates a piecewise constant signal by retaining each sample's value until the next...
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The Discrete Fourier Transform (DFT) is a fundamental tool in signal processing, extending the discrete-time Fourier transform by evaluating discrete signals at uniformly spaced frequency intervals. This transformation converts a finite sequence of time-domain samples into frequency components, each representing complex sinusoids ordered by frequency. The DFT translates these sequences into the frequency domain, effectively indicating the magnitude and phase of each frequency component present...
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Updated: Oct 3, 2025

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Wind field reconstruction with adaptive random Fourier features.

Jonas Kiessling1,2, Emanuel Ström2, Raúl Tempone3,4

  • 1H-Ai AB, Stockholm, Sweden.

Proceedings. Mathematical, Physical, and Engineering Sciences
|February 14, 2022
PubMed
Summary
This summary is machine-generated.

Random Fourier features effectively reconstructs near-surface wind fields from sparse data, outperforming traditional methods like kriging. This advanced technique offers improved accuracy for wind field analysis.

Keywords:
Metropolis algorithmflow field estimationmachine learningrandom Fourier featuresspatial interpolationwind field reconstruction

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Area of Science:

  • Geosciences
  • Atmospheric Science
  • Computational Science

Background:

  • Accurate reconstruction of near-surface wind fields is crucial for various applications, including meteorology and renewable energy.
  • Traditional spatial interpolation methods often struggle with sparse or irregularly distributed measurement data.

Purpose of the Study:

  • To evaluate the performance of random Fourier features for horizontal near-surface wind field reconstruction.
  • To compare random Fourier features against benchmark methods such as kriging and inverse distance weighting.

Main Methods:

  • Random Fourier features, a linear model, were employed to approximate the velocity field.
  • A physically motivated divergence penalty and a Sobolev norm penalty were incorporated into the model.
  • An adaptive Metropolis-Hastings algorithm was developed for sampling optimal frequency distributions.

Main Results:

  • The random Fourier features model demonstrated superior performance compared to kriging and inverse distance weighting.
  • A bound on generalization error and an optimal sampling density were derived.
  • The adaptive Metropolis-Hastings algorithm effectively sampled frequencies for the optimal distribution.

Conclusions:

  • Random Fourier features provide a robust and accurate method for reconstructing near-surface wind fields from sparse measurements.
  • The inclusion of physical constraints and advanced sampling techniques enhances the model's predictive capabilities.
  • This approach offers a promising alternative to conventional methods in atmospheric science and related fields.