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Basics of Fourier Analysis for High-Energy Astronomy
The analysis of time variability, whether fast variations on time scales well below the second or slow changes over years, is becoming more and more...
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Fourier Transform
We know from Chap. 3 that any piecewise continuous periodic function f(x) can be expanded into a Fourier...
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Fourier Methods
The changes in brightness of an astronomical source as a function of time are key probes into that source’s physics. Periodic and quasi-periodic...
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Fourier Mode Analysis Microstructured Optical Fibers
AbstractWe formulate in a nonsimplified form a method for calculating modes of microstructured optical fibers based on the representation of the...
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Fourier Series; Harmonic Analysis
In Chap. 8 we showed that a function f(x) which may be differentiated any number of times can usually be...
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Fourier Methods
The changes in brightness of an astronomical source as a function of time are key probes into that source’s physics. Periodic and quasi-periodic...
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Basics of Fourier Analysis for High-Energy Astronomy
The analysis of time variability, whether fast variations on time scales well below the second or slow changes over years, is becoming more and more...
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Fourier Quantum Process Tomography
The characterization of a quantum device is a crucial step in the development of quantum experiments. This is accomplished via Quantum Process...
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On Strengthening of the Solar f-Mode Prior to Active Region Emergence Using the Fourier-Hankel Analysis
Recent results of Singh, Raichur, and Brandenburg (
2016 ) show that the emergence of an active region (AR) can be seen in a strengthening of the...
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Fourier transform noise spectroscopy
Spectral characterization of noise environments that lead to the decoherence of qubits is critical to develo** robust quantum technologies. While...
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Fourier Series
In Sect. I.7.2 of the first book we investigated in detail how an arbitrary function f(x) can be expanded into a functional seriesFunctional series...
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Modified quantum defect theory: application to analysis of high-resolution Fourier transform spectra of neutral oxygen
AbstractThe quantum defect theory (QDT) has been successfully used to describe processes involving high-excited (Rydberg) states of atoms and...
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Short-time Fourier transform and embedding method for recurrence quantification analysis of EEG time series
Electroencephalography (EEG) allows recording of cortical activity at high temporal resolution. Creating features useful for the analysis of the EEG...
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Wide-field Fourier magnetic imaging with electron spins in diamond
Wide-field magnetic imaging based on nitrogen-vacancy (NV) centers in diamond has been shown the applicability in material and biological science....
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Hausdorff–Young Inequalities for Fourier Transforms over Cayley–Dickson Algebras
In this study, we extend Beckner’s seminal work on the Fourier transform to the domain of Cayley–Dickson algebras, establishing a precise form of the...
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Fourier and wavelet transform analysis of wavelength modulation spectroscopy signal
In the present paper, the performances of an approach based on continuous wavelet transform to demodulate wavelength modulation spectroscopy harmonic...
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Eigenvalue estimates for Fourier concentration operators on two domains
We study concentration operators associated with either the discrete or the continuous Fourier transform, that is, operators that incorporate a...
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Clifford Algebras, Quantum Neural Networks and Generalized Quantum Fourier Transform
We propose models of quantum perceptrons and quantum neural networks based on Clifford algebras. These models are capable to capture geometric...
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Short Time Quaternion Quadratic Phase Fourier Transform and Its Uncertainty Principles
In this paper, we extend the quadratic phase Fourier transform of a complex valued functions to that of the quaternion-valued functions of two...