Related papers: Super-resolution discrete-Fourier-transform spectr…
Time-resolved electronic spectra can be obtained as the Fourier transform of a special type of time correlation function known as fidelity amplitude, which, in turn, can be evaluated approximately and efficiently with the dephasing…
The efficient multiangle centered discrete fractional Fourier transform (MA-CDFRFT) [1] has proven to be a useful tool for time-frequency analysis; in this paper, we generalize the MA-CDFRFT to general M -periodic transforms, which, among…
Orthogonal Time Frequency Space (OTFS) suffers from high peak-to-average power ratio (PAPR) when the number of Doppler bins is large. To address this issue, a discrete Fourier transform spread OTFS (DFT-s-OTFS) scheme is employed by…
We propose a multi-dimensional (M-D) sparse Fourier transform inspired by the idea of the Fourier projection-slice theorem, called FPS-SFT. FPS-SFT extracts samples along lines (1-dimensional slices from an M-D data cube), which are…
Phase retrieval from phaseless short-time Fourier transform (STFT) measurements is known to be inherently unstable when measurements are taken with respect to a single window. While an explicit inversion formula exists, it is useless in…
We investigate the uniqueness of short-time Fourier transform phase retrieval problems in $L^2(\mathbb{R})$. In particular, for underlying window functions whose Fourier transform decay faster than any exponential function, we derive…
This research work focuses on the design of a high-resolution fast Fourier transform (FFT) /inverse fast Fourier transform (IFFT) processors for constraints analysis purpose. Amongst the major setbacks associated with such high resolution,…
Discrete Wavelet Transform (DWT) has been widely explored to enhance the performance of image superresolution (SR). Despite some DWT-based methods improving SR by capturing fine-grained frequency signals, most existing approaches neglect…
The use of Fourier methods in wave-front reconstruction can significantly reduce the computation time for large telescopes with a high number of degrees of freedom. However, Fourier algorithms for discrete data require a rectangular data…
Diffraction limit is manifested in the loss of high spatial frequency information that results from decay of evanescent waves. As a result, conventional far-field optics yields no information about an object's subwavelength features. Here…
In this paper we explain how to use the Fast Fourier Transform (FFT) to solve partial differential equations (PDEs). We start by defining appropriate discrete domains in coordinate and frequency domains. Then describe the main limitation of…
Developing a chip-based super-resolution imaging technique with large field-of-view (FOV), deep subwavelength resolution, and compatibility for both fluorescent and non-fluorescent samples is desired for material science, biomedicine, and…
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,…
Light scattering by tissue severely limits how deep beneath the surface one can image, and the spatial resolution one can obtain from these images. Diffuse optical tomography (DOT) is one of the most powerful techniques for imaging deep…
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…
In modern high-gain free-electron lasers, ultra-fast photon pulses designed for studying chemical, atomic and biological systems are generated from a serial of behaviors of high-brightness electron beam at the time-scale ranging from…
In many mechanical, electrical, and general physical systems evolving over time or space, spectral analysis methods as Fast Fourier Transform (FFT), Short Term Fourier Transform (STFT), Power Spectrum Density (PSD) plays a very important…
A Discrete Fourier Transform Method (DFTM) for discrimination between the signal of neutrons and gamma rays in organic scintillation detectors is presented. The method is based on the transformation of signals into the frequency domain…
Phaseless super-resolution is the problem of recovering an unknown signal from measurements of the magnitudes of the low frequency Fourier transform of the signal. This problem arises in applications where measuring the phase, and making…
The Fast Fourier Transform(FFT) is a classic signal processing algorithm that is utilized in a wide range of applications. For image processing, FFT computes on every pixel's value of an image, regardless of their properties in frequency…