Related papers: Arbitrary Transform Telescopes: The Generalization…
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…
Long-baseline interferometry at optical and near-infrared wavelengths is an emerging technology which is quickly becoming a useful tool to investigate stellar atmospheres and to compare observations with models. Stellar atmosphere models…
Spectra derived from fast Fourier transform (FFT) analysis of time-domain data intrinsically contain statistical fluctuations whose distribution depends on the number of accumulated spectra contributing to a measurement. The tail of this…
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…
Astrophotonics is the application of photonic technologies to channel, manipulate, and disperse light from one or more telescopes to achieve scientific objectives in astronomy in an efficient and cost-effective way. Utilizing photonic…
Despite being the most popular methods of data analysis, Fourier-based techniques suffer from the problem of static resolution that is currently believed to be a fundamental limitation of the Fourier Transform. Although alternative…
Graph spectral representations are fundamental in graph signal processing, offering a rigorous framework for analyzing and processing graph-structured data. The graph fractional Fourier transform (GFRFT) extends the classical graph Fourier…
Optical interference is not only a fundamental phenomenon that has enabled new theories of light to be derived but it has also been used in interferometry for the measurement of small displacements, refractive index changes and surface…
Fourier representation (FR) is an indispensable mathematical formulation for modeling and analysis of physical phenomenon, engineering systems and signals in numerous applications. In this study, we present the generalized Fourier…
Ptychography is a popular imaging technique that combines diffractive imaging with scanning microscopy. The technique consists of a coherent beam that is scanned across an object in a series of overlapping positions, leading to reliable and…
Quantum entanglement-based imaging promises significantly increased resolution by extending the spatial separation of optical collection apertures used in very-long-baseline interferometry for astronomy and geodesy. We report a table-top…
The solution of a nonlinear diffusion equation is numerically investigated using the generalized Fourier transform method. This equation includes fractal dimensions and power-law dependence on the radial variable and on the diffusion…
The fast Fourier transform, FFT, is a useful and prevalent algorithm in signal processing. It characterizes the spectral components of a signal, or is used in combination with other operations to perform more complex computations such as…
We present a graphical interface designed to demonstrate the techniques of radio interferometry used by telescopes like ALMA, e-Merlin, the JVLA and SKA, in a manner accessible to the general public. Interferometry is an observational tech-…
The Fourier-based diffraction approach is an established method to extract order and symmetry propertiesfrom a given point set. We want to investigate a different method for planar sets which works in direct spaceand relies on reduction of…
We propose a discrete fractional random transform based on a generalization of the discrete fractional Fourier transform with an intrinsic randomness. Such discrete fractional random transform inheres excellent mathematical properties of…
Due to its simultaneous deep imaging and integral field spectroscopic capability, an Imaging Fourier Transform Spectrograph (IFTS) is ideally suited to the Next Generation Space Telescope (NGST) mission, and offers opportunities for…
The graph fractional Fourier transform (GFRFT) for unitary graph Fourier transform (GFT) matrices can be interpreted through the scalar function $e^{j\alpha\theta}$ on the unit circle. Under the principal branch, its Fourier-series…
Object detection in astronomical images, generically referred to as source finding, is often performed before the object characterisation stage in astrophysical processing work flows. In radio astronomy, source finding has historically been…
The recent demonstration of a real-time direct imaging radio interferometry correlator represents a new capability in radio astronomy. However wide field imaging with this method is challenging since wide-field effects and array…