Related papers: Correcting for the alias effect when measuring the…
The Fast Fourier Transform (FFT) is a fundamental tool for signal analysis, widely used across various fields. However, traditional FFT methods encounter challenges in adjusting the frequency bin interval, which may impede accurate spectral…
We consider the problem of finding the Discrete Fourier Transform (DFT) of $N-$ length signals with known frequency support of size $k$. When $N$ is a power of 2 and the frequency support is a spectral set, we provide an $O(k \log k)$…
The matter power spectrum $P(k)$ is one of the main quantities connecting observational and theoretical cosmology. Although for a fixed redshift this can be numerically computed very efficiently by Boltzmann solvers, an analytical…
We report a new resummation procedure for the partial wave series (PWS) representation of the scattering amplitude, when a basis set of Legendre polynomials is used for the expansion. The effect of the resummation is to remove from the PWS…
We present new methods to minimize the systematic and random errors for measuring the transmission power spectrum from the Lyman-alpha forest. Sources of systematic errors explored include metal line contamination and continuum-fitting. We…
We compare the accuracy of published formulae that transform the linear perturbation theory power spectrum into the nonlinear regime against the results of an ensemble of large N-body simulations. We find that the modified transformation…
Discrete Fourier Transform (DFT) is widely used in signal processing to analyze the frequencies in a discrete signal. However, DFT fails to recover the exact Fourier spectrum, when the signal contains frequencies that do not correspond to…
Scalar diffraction calculations such as the angular spectrum method (ASM) and Fresnel diffraction, are widely used in the research fields of optics, X-rays, electron beams, and ultrasonics. It is possible to accelerate the calculation using…
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 $R_0\sim…
This paper concerns the inverse source scattering problems of recovering random sources for acoustic and elastic waves. The underlying sources are assumed to be random functions driven by an additive white noise. The inversion process aims…
Photoacoustic imaging (PAI) is a promising medical imaging modality providing the spatial resolution of ultrasound (US) imaging and the contrast of pure optical imaging. For linear-array PAI, a beamformer has to be used as the…
Optical tweezers and AFM cantilevers are often calibrated by fitting their experimental powerspectra of Brownian motion. We demonstrate here that if this is done with typical weighted least-squares methods the result is a bias of relative…
We derive and numerically implement an algorithm for estimating the 3D power spectrum of the Lyman-$\alpha$ (Ly-$\alpha$) forest flux fluctuations. The algorithm exploits the unique geometry of Ly-$\alpha$ forest data to efficiently measure…
We present a method of measuring galaxy power spectrum based on the multiresolution analysis of the discrete wavelet transformation (DWT). Since the DWT representation has strong capability of suppressing the off-diagonal components of the…
t is a known fact that near field diffraction or Fresnel diffraction calculations are difficult to perform exactly. It is in general necessary to make some approximations in order to obtain a more suitable form. In this work, a numerical…
The realm of classical phase retrieval concerns itself with the arduous task of recovering a signal from its Fourier magnitude measurements, which are fraught with inherent ambiguities. A single-exposure intensity measurement is commonly…
In many applications in compressed sensing, the measurement matrix is a Fourier matrix, i.e., it measures the Fourier transform of the underlying signal at some specified `base' frequencies $\{u_i\}_{i=1}^M$, where $M$ is the number of…
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 problem of computing the Fourier Transform of a signal whose spectrum is dominated by a small number $k$ of frequencies quickly and using a small number of samples of the signal in time domain (the Sparse FFT problem) has received…
This paper considers the problem of recovering a $k$-sparse, $N$-dimensional complex signal from Fourier magnitude measurements. It proposes a Fourier optics setup such that signal recovery up to a global phase factor is possible with very…