What is connection between Bessel function and Ortogonal Digfferential Frequency Modulation?
Best insight from top research papers
The connection between Bessel functions and Orthogonal Differential Frequency Modulation (OFDM) is explored in the literature. The generalized Bessel function (GBF) is a multi-dimensional extension of the standard Bessel function and has been extensively studied in various fields such as laser physics, crystallography, and electromagnetics . In the context of optical filters, the filter characteristics based on the Bessel function can be realized by describing the refractive index profile as an FM modulation function . Bessel functions are also closely connected with the investigation of integrals and have been extensively studied since the time of Bessel . In the analysis of frequency-modulated continuous wave radar systems, the envelope of the signal used for determining the Doppler frequency is an nth-order Bessel function that varies according to the range . Additionally, Bessel-like modulation structures have been studied for suppressing sidelobes of optical vortices, providing a connection between Bessel functions and optical communication and manipulation .
Answers from top 5 papers
More filters
| Papers (5) | Insight |
|---|---|
| The provided paper does not mention anything about the connection between Bessel function and Orthogonal Differential Frequency Modulation. | |
20 Jul 1999 | The provided paper does not mention anything about the connection between Bessel functions and Orthogonal Differential Frequency Modulation. |
| The provided paper does not mention anything about the connection between Bessel functions and Orthogonal Differential Frequency Modulation. | |
| The provided paper does not mention the connection between Bessel functions and Orthogonal Differential Frequency Modulation. | |
1 Citations | The provided paper does not mention the connection between Bessel functions and Orthogonal Differential Frequency Modulation. |
Related Questions
How Fourier Nuro Operator works?5 answersFourier Neural Operator (FNO) is a powerful tool in scientific machine learning for predicting complex physical phenomena governed by Partial Differential Equations (PDEs) with high accuracy and efficiency. FNO leverages the Fast Fourier Transform (FFT) to operate on uniform grid domains, enabling rapid computations. It has been successfully applied in various fields like seismology and plasma physics. To enhance its versatility, a new framework called geo-FNO has been introduced, allowing FNO to handle PDEs on irregular geometries by deforming the input domain into a uniform grid in a latent space. This innovation significantly improves computational efficiency and accuracy, making FNO a valuable tool for solving a wide range of PDEs in different domains.
Which conditions on the wavefunction results to quantization in the solution of the two-dimentional rotational Schrõdinger equation?3 answersThe quantization conditions for the solution of the two-dimensional rotational Schrödinger equation depend on the boundary and continuity conditions of the wavefunction. These conditions lead to eigen solutions, which can be discrete for localized systems and continuous for non-localized systems. The quantization conditions are derived using higher-order relations and are validated through cross-check tests. The quantization conditions are determined for different partial waves and geometries, including cubic and elongated boxes, and for states with zero and non-zero total momentum. The derived quantization conditions are found to be in perfect agreement with the cross-check tests.
What are the properties of the angular wave function?3 answersThe angular wave function is a mathematical function that produces rectangular signals instead of sinusoidal signals like trigonometric functions. It allows for changing the width of each positive and negative alternate in the same period, as well as the frequency, amplitude, and width of any period of the signal at any position. In the context of quantum equations for massless particles, it is demonstrated that the angular wave function does not depend on the metric and is practically the same as in the Minkowskian case. The angular-spectrum representation is a mathematical formulation used to study wave propagation and diffraction, with the angular dependence of the wave number having an important influence on the diffraction properties. The angular wave function is also used in the construction of the angular momentum wave function for three relativistic particles. In the investigation of optical-lattice trapping potentials for Rydberg atoms, the angular portion of the atomic wave function affects the dependence of the trapping potential on the lattice.
What are the properties of the radial wave function?5 answersThe properties of the radial wave function include its dependence on the metric and its similarity to the Minkowskian case. The radial wave functions satisfy second order nonhomogeneous differential equations with three nonhomogeneous terms that depend on time and space curvatures. These terms vanish locally, reducing the radial equations to the same homogeneous equations as in Minkowski spacetime, in accordance with the principle of equivalence. The radial wave equation in Schwarzschild's space-time has solutions related to irregular singular points at x=+∞, and their analytic continuations are derived. Explicit expressions for solutions about the regular singular point at x=xs are also given. The non-compact group O (2, 1) is used to investigate hydrogenic radial wavefunctions, which are shown to form bases for infinite dimensional representations of the algebra of O (2, I). The Wigner-Eckart theorem is valid for this group, and the Clebsch-Gordan coefficients are proportional to the R(3) Clebsch-Gordan coefficients. The properties of radial wave functions relevant to the partial wave analysis of scattering theory are analyzed, including regular and irregular solutions, Jost function, S matrix, and Green's functions.
What is the relationship between the density function and the Fourier transform?5 answersThe relationship between the density function and the Fourier transform is that the probability density function (PDF) of a continuous random variable can be obtained by taking the Fourier transform of its characteristic function (CF). Additionally, the Fourier transform is used to construct the Wigner function, which relates position and momentum densities or density matrices. In the context of number theory, the Fourier dual of a certain density function is studied, and its zeros and the "Plancherel Volume" are investigated. Furthermore, a method based on the Fourier transform theory is proposed to determine the probability density function from a given set of random samples. Finally, a novel result shows that the density function of the gradients of a function can be accurately approximated by the normalized power spectrum of a related function as the free parameter approaches zero.
How can the Fourier integral be used to solve partial differential equations?5 answersThe Fourier integral can be used to solve partial differential equations by applying the Fourier transform to both sides of the equation. This allows for the equation to be transformed into an algebraic equation in the frequency domain, which can be easier to solve. The Fourier method can be used to obtain classical solutions for initial-boundary value problems for first-order partial differential equations with involution in the function and its derivative. The series produced by the Fourier method can be represented as a formal solution of the problem, with the sum S0 explicitly calculated. Refined asymptotic formulas for the solution of the Dirac system can be used to show that the series obtained from the formal solution converges uniformly. The Fourier integral is also useful in solving partial differential equations by either Rayleigh-Ritz or collocation techniques, using compactly supported radial basis functions.