Related papers: Correcting for the alias effect when measuring the…
We present a new deterministic algorithm for the sparse Fourier transform problem, in which we seek to identify k << N significant Fourier coefficients from a signal of bandwidth N. Previous deterministic algorithms exhibit quadratic…
Denote by $p(k)$ the limit, as $n \rightarrow \infty$, of the probability that a random permutation on a set of size $n$ has an invariant set of size $k$. We give an asymptotic formula for $p(k)$, showing that it is asymptotically…
One of the major difficulties limiting ground-based direct imaging of exoplanets with adaptive optics is quasi-static speckles in the science camera (SC) that obscure the planetary image. These speckles are caused by aberrations, called…
While spike trains are obviously not band-limited, the theory of super-resolution tells us that perfect recovery of unknown spike locations and weights from low-pass Fourier transform measurements is possible provided that the minimum…
Photoacoustic image reconstruction often assumes that the restriction of the acoustic pressure on the detection surface is given. However, commonly used detectors often have a certain directivity and frequency dependence, in which case the…
An aperiodic (low frequency) spectrum may originate from the error term in the mean value of an arithmetical function such as M\"obius function or Mangoldt function, which are coding sequences for prime numbers. In the discrete Fourier…
A grid-based real-space implementation of the Projector Augmented Wave (PAW) method of P. E. Blochl [Phys. Rev. B 50, 17953 (1994)] for Density Functional Theory (DFT) calculations is presented. The use of uniform 3D real-space grids for…
We discuss the determination of the linear power spectrum of dark matter fluctuations from measurements of the transmitted flux Ly-alpha Forest power spectrum. We show that at most scales probed by current measurements, the flux power…
This paper details the purpose, difficulties, theory, implementation, and results of developing a Fast Fourier Transform (FFT) using the prime factor algorithm on an embedded system. Many applications analyze the frequency content of…
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 nonlinear Fourier transform has the potential to overcome limits on performance and achievable data rates which arise in modern optical fiber communication systems when nonlinear interference is treated as noise. The periodic nonlinear…
Instruments using arrays of many bolometers have become increasingly common in the past decade. The maps produced by such instruments typically include the filtering effects of the instrument as well as those from subsequent steps performed…
Multiple hypothesis testing is a significant problem in nearly all neuroimaging studies. In order to correct for this phenomena, we require a reliable estimate of the Family-Wise Error Rate (FWER). The well known Bonferroni correction…
We show that the `shot noise' bias in angular clustering power spectra observed from discrete samples of points is not noise, but rather a known additive contribution that naturally arises due to degenerate pairs of points. In particular,…
In this paper, we propose a new regression-based algorithm to compute Graph Fourier Transform (GFT). Our algorithm allows different regularizations to be included when computing the GFT analysis components, so that the resulting components…
The power spectrum of finite-temperature quantum electromagnetic fluctuations produced by elementary charge carriers under the influence of external electric field is investigated. It is found that under the combined action of the photon…
Measurement devices always add noise to the signal of interest and it is necessary to evaluate the variance of the results. This article focuses on stationary random processes whose Power Spectrum Density is a power law of frequency. For…
We show how to estimate the covariance of the power spectrum of a statistically homogeneous and isotropic density field from a single periodic simulation, by applying a set of weightings to the density field, and by measuring the scatter in…
We compute the weak lensing convergence power spectrum, $C^{\kappa\kappa}(\theta)$, in a dust-filled universe using fully non-linear general relativistic simulations. The spectrum is then compared to more standard, approximate calculations…
We explain why aliasing can be detected in a generic temporally-sampled stationary signal process. We then define a concept of stationarity that makes sense for single waveforms. (This is done without assuming that the waveform is a sample…