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FFT algorithm is one of the most applied algorithmsin digital signal processing. Digital signal processing hasgradually become important in biomedical application. Herehardware implementation of FFTs have found useful appli-cations for…
We present $\mathcal{O}(N^2)$ estimators for the small-scale power spectrum and bispectrum in cosmological simulations. In combination with traditional methods, these allow spectra to be efficiently computed across a vast range of scales,…
Space-based direct imaging provides prospects for detection and spectral characterization of exoplanets at optical and near-infrared wavelengths. Integral field spectrographs (IFS) have been historically baselined for these mission…
Ultra-light dark matter candidates, such as axions and dark photons, particularly within the mass range of $\mu$eV to meV, have garnered significant research interest. However, the effectiveness of existing experiments is often hindered by…
Feature selection is generally used as one of the most important preprocessing techniques in machine learning, as it helps to reduce the dimensionality of data and assists researchers and practitioners in understanding data. Thereby, by…
Large-scale structure distorts the images of background galaxies, which allows one to measure directly the projected distribution of dark matter in the universe and determine its power spectrum. Here we address the question of how to…
In this paper we consider the problem of approximating function evaluations $f(\boldsymbol x_j)$ at given nonequispaced points $\boldsymbol x_j$, $j=1,\dots N$, of a bandlimited function from given values $\hat{f}(\boldsymbol k)$,…
Fourier transform spectroscopy (FTS) has been widely used as an analytical tool for many applications in science and engineering. In this paper, we describe the operation principle and practical implementation of an FTS prototype. First,…
Signal decomposition is an effective tool to assist the identification of modal information in time-domain signals. Two signal decomposition methods, including the empirical wavelet transform (EWT) and Fourier decomposition method (FDM),…
While conventional power system protection isolates faulty components only after a fault has occurred, fault prediction approaches try to detect faults before they can cause significant damage. Although initial studies have demonstrated…
Structure formation at small cosmological scales provides an important frontier for dark matter (DM) research. Scenarios with small DM particle masses, large momenta or hidden interactions tend to suppress the gravitational clustering at…
The Fractional Fourier Transform (FRT) corresponds to an arbitrary-angle rotation in the phase space, e.g. the time-frequency (TF) space, and generalizes the fundamentally important Fourier Transform. FRT applications range from classical…
Fourier transform spectroscopy (FTS) has been widely used in a variety of fields in research, industry, and medicine due to its high signal-to-noise ratio, simultaneous acquisition of signals in a broad spectrum, and versatility for…
The analysis of the Lyman-alpha forest of absorption lines in quasar spectra has emerged as a potentially powerful technique to constrain the linear matter power spectrum. In most previous work, the amplitude of the ionizing background was…
Accurate beam alignment is a critical challenge in XL-MIMO systems, especially in the near-field regime, where conventional far-field assumptions no longer hold. Although 2D grid-based codebooks in the polar domain are widely accepted for…
We measure the power spectrum of galaxy clustering in real space from the APM Galaxy Survey. We present an improved technique for the numerical inversion of Limber's equation that relates the angular clustering of galaxies to an integral…
We present two related techniques to measure the two-point correlation function and the power spectrum with edge correction in any spatial dimensions. The underlying algorithm uses fast Fourier transforms for calculating the two-point…
The three-dimensional galaxy power spectrum is a powerful probe of primordial non-Gaussianity and additional general relativistic effects, which become important on large scales. At the same time, wide-angle (WA) effects due to differing…
Redshift-space distortions in galaxy surveys happen along the radial direction, breaking statistical translation invariance. We construct estimators for radial distortions that, using only Fast Fourier Transforms (FFTs) of the overdensity…
Many interesting and fundamentally practical optimization problems, ranging from optics, to signal processing, to radar and acoustics, involve constraints on the Fourier transform of a function. It is well-known that the {\em fast Fourier…