Related papers: Non-uniform sampled scalar diffraction calculation…
The Special Affine Fourier Transformation(SAFT), which generalizes several well-known unitary transformations, has been demonstrated as a valuable tool in signal processing and optics. In this paper, we explore the multivariate dynamical…
Nonlinear Fourier division Multiplexing (NFDM) can be realized from modulating the discrete nonlinear spectrum of an $N$-solitary waveform. To generate an $N$-solitary waveform from desired discrete spectrum (eigenvalue and discrete…
The Fast Fourier Transform (FFT) is one of the most widely used algorithms in high performance computing, with critical applications in spectral analysis for both signal processing and the numerical solution of partial differential…
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…
Fourier domain methods are fast algorithms for SAR imaging. They typically involve an interpolation in the frequency domain to re-grid non-uniform data so inverse fast Fourier transforms can be performed. In this paper, we apply a frame…
The design of starshades, i.e. external occulters for stellar coronography, relies on the fast and precise computation of their associated diffraction patterns of incoming plane waves in the telescope aperture plane. We present here a…
Image subtraction is essential for transient detection in time-domain astronomy. The point spread function (PSF), photometric scaling, and sky background generally vary with time and across the field-of-view for imaging data taken with…
In this work, we implement a relatively new analytical technique, the Improved Amplitude-Frequency Formulation (IAFF) method, approach for solving accurate approximate analytical solutions for strong nonlinear oscillators, which may contain…
In this article, we develop comprehensive frequency domain methods for estimating and inferring the second-order structure of spatial point processes. The main element here is on utilizing the discrete Fourier transform (DFT) of the point…
An integrated photonic circuit architecture to perform a modified-convolution operation based on the Discrete Fractional Fourier Transform (DFrFT) is introduced. This is accomplished by utilizing two nonuniformly-coupled waveguide lattices…
In this article, we present an $O(N \log N)$ rapidly convergent algorithm for the numerical approximation of the convolution integral with radially symmetric weakly singular kernels and compactly supported densities. To achieve the reduced…
Fourier reconstruction algorithms significantly outperform conventional back-projection algorithms in terms of computation time. In photoacoustic imaging, these methods require interpolation in the Fourier space domain, which creates…
The Discrete Fourier Transform (DFT) is central to the analysis of uniformly sampled signals, yet many practical applications involve non-uniform sampling, requiring the Non-Uniform Discrete Fourier Transform (NUDFT). While quantum…
The short-time Fourier transform (STFT) usually computes the same number of frequency components as the frame length while overlapping adjacent time frames by more than half. As a result, the number of components of a spectrogram matrix…
We implement an efficient method of computation of two dimensional Fourier-type integrals based on approximation of the integrand by Gaussian radial basis functions, which constitute a standard tool in approximation theory. As a result, we…
The principles and practice of astronomical imaging Fourier transform spectroscopy (FTS) at far-infrared wavelengths are described. The Mach-Zehnder interferometer design has been widely adopted for current and future imaging FTS…
We propose a multi-shell sampling grid and develop corresponding transforms for the accurate reconstruction of the diffusion signal in diffusion MRI by expansion in the spherical polar Fourier (SPF) basis. The transform is exact in the…
We investigate a modified split-step Fourier method (SSFM) by including low-pass filters in the linear steps. This method can simultaneously achieve a higher simulation accuracy and a slightly reduced complexity.
We describe an approach based on compressive-sampling which allows for a considerable reduction in the acquisition time in Fourier-transform spectroscopy. In this approach, an N-point Fourier spectrum is resolved from much less than N…
Fourier optics is a powerful and efficient tool for solving many diffraction problems, but relies on the assumption of scalar diffraction theory and ignores the three-dimensional structure and material properties of the diffracting element.…