0
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0answers
19 views

stroboscope effect

I have a disc with a line drawn on one of his radius that is turning with frequency $f$, and I want to sample the place of the line to find the frequency of the disc. So we know from the ...
0
votes
1answer
30 views

please help me understand the lecture note? heat equation and fourier series

I don't quite understand equation 3.73 and 3.74. To get $T(x,t)$ I thought I had to multiply F and G. How does that give equation 3.73? I got G as e^{stuff} as in the last bit of equation 3.73. ...
0
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2answers
31 views

Heat equation. Find $B_n$ (using boundary conditions?)

Can anyone help me with (b)(i)? I've done the first part of it. I've tried putting some boundary conditions in but cannot find $B_n$ What fact should I use? An infinite slab of material, of ...
1
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1answer
64 views

How to convert FFT magnitude of square wave to dBm?

I wish to convert the FFT magnitude of square wave into dBm. I use FFT to covert voltage of square wave to a complex number, then i absolute the complex number into magnitude. Then i divide the ...
1
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0answers
71 views

The Envelope (wave front) of a span of plane waves.

Imagine we have for every real direction $\mathbf n \in \mathbb R^3$ a plane wave, be it either quantum, eletric, magnetic, acoustic or in my case some sheets of paper I am holding up. Each of these ...
0
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1answer
98 views

Deconvolution of a convolution product with $Ax\ /\ (x^2+l^2)^{3/2}$

This is not a homework, and I have no idea whether it could be one. It is only a request for help, as I do not have any experience using Fourier transform. The origin of the problem is from physics. ...
3
votes
0answers
331 views

Solve a differential equation using Fourier series

Assume I have a second order differential equation $\ddot{x} = F(x,\dot{x})$ (or an equivalent equation of first order) and that I know there is a periodic solution to it (for simplicity's sake, ...
3
votes
1answer
143 views

Why does dimensional analysis seem to fail in determining the scaling of the Fourier transform?

In his book Street-Fighting Mathematics, at pag. 7, S. Mahajan uses the technique of dimensional analysis to obtain very quickly the following result: $$\int_{-\infty}^{\infty}e^{-ax^2}\, dx = ...
1
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1answer
438 views

Can the differentiating and squaring process in the cochlea explain a reported dichotic stimulation experiment?

On this math.stackexchange on url What is Octave Equivalence? in an answer on the related ( octave equivalence ) question is stated: Mathematically, this signifies that the mammalian cochlea ...
1
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0answers
150 views

Fourier transform of $\frac{g_i}{e^{\frac{\epsilon_i-\mu}{kT}}-1}$? Not Gaussian like with Fermi-Dirac statistics?

This equation $\bar n_i=\frac{g_i}{e^{\frac{\epsilon_i-\mu}{kT}}-1}$ is Fermi-Dirac statistics where variables are defined here. The classical equation i.e. the Maxwell Boltzman equation is Gaussian ...
1
vote
0answers
60 views

Convolutions of Path Integrals of Gaussian Functions

I was looking at a question on a physics forum (http://physics.stackexchange.com/questions/45955/splitting-light-into-colors-mathematical-expression-fourier-transforms) and I wanted a more ...
2
votes
1answer
225 views

Finding the 'inhomogeneous' plane wave solutions of the wave equation via Fourier analysis

When one solves the wave equation $$ ( \partial_t^2 - v^2 \nabla^2) \mathbf{E}(\mathbf{x},t) = 0 $$ in $\mathbb{R}^3 \times \mathbb{R} $ using the Fourier transform method, the general solution is ...
4
votes
0answers
64 views

Why are linear functions the natural analogue of exponential functions in a tropical semiring?

I was reading a blog post on the Fourier transform and the Legendre transform as being the same thing over different semirings, in which the author says It's not obvious how to interpret the ...
4
votes
1answer
263 views

Fourier (Hankel?) transform of a discrete set of radial points (question from a chemist!)

I'm sorry because I'm not a mathematician so that my question may look a little bit messy. I have tabulated values [1] of a 3 dimensional radial function $f(r)$: ...
2
votes
1answer
178 views

Trouble deriving DE for fourier transform from DE of function

I am trying to derive an equation which is a standard result in physics (the momentum space Schrödinger equation). (Background: The wavefunction is a complex valued function of position coordinates ...
1
vote
3answers
432 views

Fourier analysis for waves

I'm studying physics, so I'm sorry if I'll write some inexact things in this post. I wish you can understand me. If we have 1D wave equation: $$\frac{\partial^2 \psi}{\partial ...