The fourier-transform tag has no wiki summary.
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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 ...
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Physical interpretation of Parseval's theorem
I have read that Parseval's theorem, relating the norm of a function $f$ and the norm of its Fourier transform $g(k)$:
\begin{equation}
\int |f(x)|^2 dx=\int|g(k)|^2 dk
\end{equation}
has the ...
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Uncertainty Principle for a Totally Localized Particle
If a particle is totally localized at $x=0$, its wave function $\Psi(x,t)$ should be a Dirac delta function $\delta(x)$. Accordingly, its Fourier transform $\Phi(p,t)$ would be a constant for all $p$, ...
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Fourier Methods in General Relativity
I am looking for some references which discuss Fourier transform methods in GR. Specifically supposing you have a metric $g_{\mu \nu}(x)$ and its Fourier transform $\tilde{g}_{\mu \nu}(k)$, what does ...
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Expressing a particle's matter wave in terms of its momentum
I'm following Zettili's QM book and on p. 39 the following manipulation is done,
Given a localized wave function (called a wave packet), it can be expressed as $$\psi(x,t) = \frac{1}{\sqrt{ 2 \pi}} ...
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How to distinguish female and male voices via Fourier analysis?
What makes one, without looking, be able to identify the gender of the talker as male or female?
I mean if we Fourier analysed the voice of males and females, how the 2 spectrums are different which ...
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Conjugate Variables and Fourier Transforms in Classical Physics
Let q be a generalized coordinate with a conjugate momentum p and a potential resulting in a periodic motion of q. What is the meaning of the Fourier transform of q(t) over its period? Can this be ...
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Sine wave with a constant period: what else is constant? [closed]
Which statistic that you can calculate on a window remains constant on a sine wave with a constant period? This is for a window function for a proprietary filter.
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Does a finite wave necessarily have to be non-monochromatic in reality?
Does a finite wave necessarily have to be non-monochromatic in reality, or is that implication just a result of the mathematical analysis? I always wonder at these sort of things that come out of a ...
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Duality and Fourier Transforms [closed]
I read that
$(FF(f))(x)=2\pi f(-x)$, where $F$ is the Fourier transform
and $F(f(x-a))(k)=\exp(-ika) X(k)$ where $X(k)=F(f(x))$
implies $F(\exp(iax)f(x))(k)=X(k-a)$.
But I don't see how that is ...
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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 ...
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Why higher frequencies in Fourier series are more suppressed than lower frequencies?
One can expand any periodic function in sines and cosines. When calculating the coefficients $a_0$, $a_n$, and $b_n$ one find that $a_1>a_2>...>a_n>...$, similarly for $b_n$.
Is there an ...
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How does the Fourier Transform invert units?
I don't really understand how units work under operations like derivation and integration. In particular, I am interested in understanding how the Fourier transform gives inverse units (i.e. time ...
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Can one canonical conjugate variable be considered to be the “frequency” of the other one? (which could be a “wavelength”)?
So, from http://en.wikipedia.org/wiki/Conjugate_variables#Derivatives_of_action, we have...
The energy of a particle at a certain event is the negative of the derivative of the action along a ...
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Simulating eye diagrams
I'm trying to figure out how to simulate eye diagrams for communications systems using Python. I'm not sure I have the theory down completely, though. From what I could figure out using some old ...
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What is the specific meaning of “Fourier frequency” (as opposed to simply “frequency”)?
I've noticed that many journal articles (in optics) use the phrase "Fourier frequency" to describe, well, the frequency of something.
Google scholar search for "Fourier frequency".
Example:
...
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What is the meaning of the Fourier transform of Feynman propagator?
I know $K(a,b,t)$ is the probability amplitude of find a particle that starts at point a in b in a time t later. There is also an expression that sometimes is called green function:
...
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Very simple example of the way the Fourier transform is used in quantum mechanics?
According to a book I'm reading, the Fourier transform is widely used in quantum mechanics (QM). That came as a huge surprise to me. (Unfortunately, the book doesn't go on to give any simple examples ...
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Using Fourier Transforms to Solve Systems with springs of high frequency
I'm trying to numerically solve the differential equations of motion in a system with multiple springs of very high frequency. Because the solution is often a combination of rapidly-oscillating sine ...
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“Optically performed” Fourier Transform
This article says that they are only able to achieve such extremely high fiberoptic data rates because the multiplex light and then use a Fourier Transform to split it up again. But they say that ...
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Finding $\psi(x)$ from Fourier modes
In quantum physics we've defined:
$$ \psi (x) = \sqrt{ \dfrac{1}{2 \pi \hbar} } \int^{ \infty }_{-\infty } \phi (p) \exp \left( i \dfrac{px}{ \hbar} \right) dp $$
Now,
$$a(k) \equiv \sqrt{ \hbar } ...
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Why is the bispectrum not commonly used in experimental physics?
Power spectra, coherence spectra, and linear transfer functions are ubiquitous tools of experimental physics. However, our instruments often retain small nonlinear effects which can contaminate ...
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What is the relation between position and momentum wavefunctions in quantum physics?
I have read in a couple of places that $\psi(p)$ and $\psi(q)$ are Fourier transforms of one another (e.g. Penrose). But isn't a Fourier transform simply a decomposition of a function into a sum or ...
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Does this statement make any sense?
I am asking this question completely out of curiosity. The other day, my roommate, by mistake, used 'Light year' as a unit of time instead of distance. When I corrected him (pedantic, much), he said ...
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How do I compute the eigenfunctions of the Fourier Transform? [closed]
I read today (ref) that the Continuous Fourier Transform has four eigenvalues: +1, +i, -1, and -i. Associated with each eigenvalue is a space of eigenfunctions: functions which retain their form ...
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Fourier transformation in nature/natural physics?
I just came from a class on Fourier Transformations as applied to signal processing and sound. It all seems pretty abstract to me, so I was wondering if there were any physical systems that would ...
