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The Fractional Fourier Transform (FRT) corresponds to an arbitrary-angle rotation in the phase space, e.g. the time-frequency (TF) space, and generalizes the fundamentally important Fourier Transform. FRT applications range from classical…
We propose a simpler derivation of the probability density function of Feller Diffusion using the Fourier Transform and solving the resulting equation via the Method of Characteristics. We also discuss simulation algorithms and confirm key…
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…
In this paper, we extend our method [1] for FMCW radar mutual interference mitigation (IM) based on the discrete fractional Fourier transform (DFrFT). Firstly, we propose a radar signal processing chain including our DFrFT-based IM for…
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…
An adaptive time-frequency representation (TFR) with higher energy concentration usually requires higher complexity. Recently, a low-complexity adaptive short-time Fourier transform (ASTFT) based on the chirp rate has been proposed. To…
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…
We present an accurate and efficient method to calculate the effect of random fluctuations of the local field at the muon, for instance in the case muon diffusion, within the framework of the strong collision approximation. The method is…
This study puts forward a generalization of the short-time Fourier-based Synchrosqueezing Transform using a new local estimate of instantaneous frequency. Such a technique enables not only to achieve a highly concentrated time-frequency…
The interference of fluorescence signals and noise remains a significant challenge in Raman spectrum analysis, often obscuring subtle spectral features that are critical for accurate analysis. Inspired by variational methods similar to…
Biological soft tissues encountered in clinical and pre-clinical imaging mainly consist of light element atoms, and their composition is nearly uniform with little density variation. Thus, x-ray attenuation imaging suffers from low image…
This work proposes a novel technique for the numerical calculus of the fractal dimension of fractal objects which can be represented as a closed contour. The proposed method maps the fractal contour onto a complex signal and calculates its…
A scheme to a complex-valued acquisition of the Fourier transform imaging was proposed. The main idea is to project the real and the imaginary parts of a diffraction field to intensity distributions respectively. The whole procedure was…
I discuss the nature of a Fractional Discrete Fourier Transform (FrDFT) described algorithmically by a combination of chirp transforms and ordinary DFTs. The transform is shown to be consistent with a continuous two-dimensional rotation…
In this paper, a new variant to fractional signal processing is proposed known as the Reduced Order Fractional Fourier Transform. Various properties satisfied by its transformation kernel is derived. The properties associated with the…
In many practical applications, spatial data are often collected at areal levels (i.e., block data) and the inferences and predictions about the variable at points or blocks different from those at which it has been observed typically…
Intrinsic spectrum that results from the coupling of spontaneous emission in a laser cavity, can determine the energy concentration and coherence of lasers, which is crucial for the optical high-precision measurement. Up to now, it is hard…
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…
Recent developments in machine learning and signal processing have resulted in many new techniques that are able to effectively capture the intrinsic yet complex properties of hyperspectral imagery. Tasks ranging from anomaly detection to…
This paper develops a high-accuracy algorithm for time fractional wave problems, which employs a spectral method in the temporal discretization and a finite element method in the spatial discretization. Moreover, stability and convergence…