0
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0answers
4 views

Verification of Fourier transformationn of Io-sinh function [migrated]

I try to match. What could not match $I_o-\sinh$ pair developed by Ben Logan, transform pair also published in The Practical Application of the Fourier Integral Campbell, George A .Sir J.F. Kaiser ...
0
votes
0answers
18 views

Question on envelope-carrier description of traveling wave

I'm doing a research internship in attosecond physics right now, and one of the really important things in the field is the description of a propagating laser pulse as the combination of a slowly (or ...
3
votes
1answer
93 views

Plane wave complex notation

As far as I know, the function: $$ \vec{E}(\vec{r},t)=\vec{E_0}\cdot e^{i(\vec{k}\cdot \vec{r}-\omega t)} \hspace{2cm}(1) $$ is a mathematical solution of the wave equation: $$ \nabla^2 ...
2
votes
1answer
62 views

Far Field Diffraction of EM waves: what does the zero frequency signify?

If you have a system of independently radiating electrons/point-charges, the far field distribution of the EM waves can be approximated by the fraunhoffer diffraction integral, or simply by the ...
0
votes
0answers
44 views

Phased array radar equations

Suppose we have several antennae to transmit and receive radio waves. What should one transmit, and what kind of equations are used to compute $reflectivity(\vec{x})$ for points in space from a given ...
4
votes
1answer
325 views

Fourier transformation, electric field and magnetic field to have a shielding lattice against particles

With Fourier-Series Expansion, we can write a function as sum of many non-repating different frequncied different amplituded sine and cosine functions. Lets assume we know electric-field and ...
2
votes
0answers
133 views

Fourier Transform of ribbon's beam Electric Field

I have a monochromatic ribbon beam with $E(x)e^{i(kz-\omega t)}$ being the electric field's amplitude. I want to show that the lowest order approximation in terms of plane waves is ...
3
votes
5answers
3k views

Why are AC quantities represented by sine waves always?

Usually we use a sinusoidal wave form to represent a alternating quantity. Why not a cosinusoidal wave or a ramp wave form? In sine wave forms we can indicate the maximum and minimum amplitude and ...
2
votes
3answers
285 views

Energy stored in space/frequency electric field

I've come across a problem with finding the energy stored in time/frequency electric field. In space/time we have (taking $\epsilon = 1$) $$ Energy = \frac{1}{2} \int_V |\mathbf{E}(\mathbf{x},t)|^2 ...
0
votes
2answers
952 views

What's the physical meaning of the Fourier transform of magnetic flux density?

I have here below the distribution of the magnetic flux density $B$ across a 1 pole pitch in the airgap of a synchronous machine. The horizontal axis represents the distance along the arc length ...
5
votes
3answers
1k views

Can Laplace's equation be solved using Fourier transform instead of Fourier series?

Sorry for the long text, but I am unable to make my question more compact. Any periodic function can be Fourier expanded. Usually, they say in mathematical physics books, if the function is not ...