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A charge-density-wave (CDW) is characterized by a dynamical order parameter consisting of a time-dependent amplitude and phase, which manifest as optically-active collective modes of the CDW phase. Studying the behaviour of such collective…
Wave turbulence in a thin elastic plate is experimentally investigated. By using a Fourier transform profilometry technique, the deformation field of the plate surface is measured simultaneously in time and space. This enables us to compute…
A discrete complexified quaternion Fourier transform is introduced. This is a generalization of the discrete quaternion Fourier transform to the case where either or both of the signal/image and the transform kernel are complex…
Gravitational wave astrophysics has only just begun, and as current detectors are upgraded and new detectors are built, many new, albeit faint, features in the signals will become accessible. One such feature is the presence of…
Two-dimensional charge density wave (CDW) materials received much attention for high responsivity and broadband photodetection in recent years, due to their collective electron transport and narrow bandgap. However, the high dark current…
The capability to isolate one to few unit-cell thin layers from the bulk matrix of layered compounds opens fascinating prospects to engineer novel electronic phases. However, a comprehensive study of the thickness dependence and of…
The state-of-the-art automotive radars employ multidimensional discrete Fourier transforms (DFT) in order to estimate various target parameters. The DFT is implemented using the fast Fourier transform (FFT), at sample and computational…
We propose a novel method for detecting gravitational waves (GW), where a light signal emitted from a distant star interacts with a local (also distant) GW source and travels towards the Earth, where it is detected. While traveling in the…
The wavelet scattering transform (WST) has recently gained attention in the context of large-scale structure studies, being a possible generator of summary statistics encapsulating non-Gaussianities beyond the reach of the conventional…
This paper presents a new approach for tackling the shift-invariance problem in the discrete Haar domain, without trading off any of its desirable properties, such as compression, separability, orthogonality, and symmetry. The paper…
We present the Fourier Transform of a continuous gravitational wave. We have analysed the data set for one day observation time and our analysis is applicable for arbitrary location of detector and source. We have taken into account the…
Spatial uctuations of spin density wave (SDW) and charge density wave (CDW) in chromium have been compared by combining coherent and simultaneous X-ray diffraction experiments. Despite their close relationship, spatial fluctuations of the…
The Fractional Fourier Transform is a ubiquitous signal processing tool in basic and applied sciences. The Fractional Fourier Transform generalizes every property and application of the Fourier Transform. Despite the practical importance of…
Time-frequency representations (TFRs) of signals, such as the windowed Fourier transform (WFT), wavelet transform (WT) and their synchrosqueezed variants (SWFT, SWT), provide powerful analysis tools. However, there are many important issues…
The usual fluid equations describing the large-scale evolution of mass density in the universe can be written as local in the density, velocity divergence, and velocity potential fields. As a result, the perturbative expansion in small…
The ubiquity of sequences in many domains enhances significant recent interest in sequence learning, for which a basic problem is how to measure the distance between sequences. Dynamic time warping (DTW) aligns two sequences by nonlinear…
Many signals on Cartesian product graphs appear in the real world, such as digital images, sensor observation time series, and movie ratings on Netflix. These signals are "multi-dimensional" and have directional characteristics along each…
We established a new method called Discrete Weierstrass Fourier Transform, a faster and more generalized Discrete Fourier Transform, to approximate discrete data. The theory of this method as well as some experiments are analyzed in this…
The dynamics of phase transitions (PT) in quantum field theories at finite temperature is most accurately described within the framework of dimensional reduction. In this framework, thermodynamic quantities are computed within the…
This paper establishes connections between the group-Fourier transform and the geometry of measures in the Heisenberg group. Firstly, it is shown that if the Fourier transform of a compactly supported, finite, Radon measure is square…