相关论文: Accurate estimators of power spectra in N-body sim…
The power spectrum, as a statistic in Fourier space, is commonly numerically calculated using the fast Fourier transform method to efficiently reduce the computational costs. To alleviate the systematic bias known as aliasing due to the…
In measuring the power spectrum of the distribution of large numbers of dark matter particles in simulations, or galaxies in observations, one has to use Fast Fourier Transforms (FFT) for calculational efficiency. However, because of the…
Estimators for $n$-point clustering statistics in Fourier-space demand that modern surveys of large-scale structure be transformed to Cartesian coordinates to perform Fast Fourier Transforms (FFTs). In this work, we explore this…
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,…
The computational efficiency of many neural operators, widely used for learning solutions of PDEs, relies on the fast Fourier transform (FFT) for performing spectral computations. As the FFT is limited to equispaced (rectangular) grids,…
We present a spectrally accurate, efficient FFT-based method for the three-dimensional free-space Poisson equation with smooth, compactly supported sources. The method adopts a super-potential formulation: we first compute the convolution…
Efficient estimators of Fourier-space statistics for large number of objects rely on Fast Fourier Transforms (FFTs), which are affected by aliasing from unresolved small scale modes due to the finite FFT grid. Aliasing takes the form of a…
The usual fluid equations describing the large-scale evolution of mass density in the universe can be written as local in the density, velocity divergence, and velocity potential fields. As a result, the perturbative expansion in small…
Because of mass assignment onto grid points in the measurement of the power spectrum using the Fast Fourier Transform (FFT), the raw power spectrum $\la |\delta^f(k)|^2\ra$ estimated with FFT is not the same as the true power spectrum…
Fast Fourier transform based estimators are formulated for measuring momentum power spectra, including the auto power spectra of the momentum, the momentum divergence, and the cross spectrum of density fluctuation and momentum divergence.…
Fourier methods are fundamental tools to analyze random fields. Statistical structures of homogeneous Gaussian random fields are completely characterized by the power spectrum. In non-Gaussian random fields, polyspectra, higher-order…
We present a new and highly efficient algorithm for computing a power spectrum made from evenly spaced data which combines the noise-reducing advantages of the weighted fit with the computational advantages of the Fast Fourier Transform…
We present a new class of estimators for computing small-scale power spectra and bispectra in configuration-space via weighted pair- and triple-counts, with no explicit use of Fourier transforms. Particle counts are truncated at $R_0\sim…
Fourier transform methods are used to analyze functions and data sets to provide frequencies, amplitudes, and phases of underlying oscillatory components. Fast Fourier transform (FFT) methods offer speed advantages over evaluation of…
We present an algorithm for quickly generating multiple realizations of N-body simulations to be used, for example, for cosmological parameter estimation from surveys of large-scale structure. Our algorithm uses a new method to resample the…
This paper introduces a generalised 3rd-order Spectral Representation Method for the simulation of multi-dimensional stochastic fields with asymmetric non-linearities. The simulated random fields satisfy a prescribed Power Spectrum and…
Power spectrum estimation is an important tool in many applications, such as the whitening of noise. The popular multitaper method enjoys significant success, but fails for short signals with few samples. We propose a statistical model…
The state-of-the-art automotive radars employ multidimensional discrete Fourier transforms (DFT) in order to estimate various target parameters. The DFT is implemented using the fast Fourier transform (FFT), at sample and computational…
Measurements of line-of-sight dependent clustering via the galaxy power spectrum's multipole moments constitute a powerful tool for testing theoretical models in large-scale structure. Recent work shows that this measurement, including a…
We develop a general method for power spectrum analysis of three dimensional redshift surveys. We present rigorous analytical estimates for the statistical uncertainty in the power and we are able to derive a rigorous optimal weighting…