The fourier-transform tag has no wiki summary.
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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 ...
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2answers
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Was uncertainty principle inferred by Fourier analysis?
I would like to know: did Heisenberg chance upon his Uncertainty Principle by performing Fourier analysis of wavepackets, after assuming that electrons can be treated as wavepackets?
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Does light have timbre?
Timbre is a property associated with the shape of a sound wave, that is, the coefficients of the discrete Fourier transform of the corresponding signal. This is why a violin and a piano can each play ...
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1answer
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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 ...
7
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1answer
355 views
Calculating diffraction patterns using FFT
I'm trying to write a piece of code that calculates a diffraction pattern similar to an X-ray experiment using a FFT.
From my knowledge, the diffraction pattern for point particles can be calculated ...
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2answers
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Evaluating propagator without the epsilon trick
Consider the Klein–Gordon equation and its propagator:
$$G(x,y) = \frac{1}{(2\pi)^4}\int d^4 p \frac{e^{-i p.(x-y)}}{p^2 - m^2} \; .$$
I'd like to see a method of evaluating explicit form of $G$ ...
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What does the Canonical Commutation Relation (CCR) tell me about the overlap between Position and Momentum bases?
I'm curious whether I can find the overlap $\langle q | p \rangle$ knowing only the following:
$|q\rangle$ is an eigenvector of an operator $Q$ with eigenvalue $q$.
$|p\rangle$ is an eigenvector of ...
6
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2answers
597 views
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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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 ...
6
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1answer
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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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3answers
349 views
Physics of a guitar
I understand that when you pluck a guitar string, then a bunch of harmonic frequencies are produced rather than just the frequency of the desired note.
If this is true, why does C2 sound so different ...
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4answers
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Optics of the eye - do we see Fourier transforms?
I've recently been learning about Fourier optics, specifically, that a thin lens can produce the Fourier transform of an object on a screen located in the focal plane.
With this in mind, does the ...
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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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3answers
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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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1answer
139 views
What's the physical significance of using fourier transform for diffraction?
I am studying some basic idea of diffraction and there mention in far field, the diffraction pattern could be understood by Fourier transform. But I just don't understand what's the physical fact for ...
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Modeling stochastic process with frequency-dependent power spectrum
I'm trying to model of Johnson-Nyquist noise propagation in a nonlinear circuit. An ideal (linear) resistor can be modeled very nicely by the Fokker-Planck equation (equivalently, the drift-diffusion ...
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1answer
171 views
Fourier Transform on a Riemannian Manifold
The question is quite simple: What would be the definition of Fourier Transform (and it's inverse) on a Riemannian Manifold?
I've found that a similar question has been asked at Mathematics.SE but ...
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1answer
200 views
Intuition behind Fourier transformed spaces
Intuitively I've been able to understand a Fourier transform a change-of-basis formula - you're basically moving from position to momentum basis or from time to frequency - but what does it mean that ...
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Canonical Commutation Relations
Is it logically sound to accept the canonical commutation relation (CCR)
$$[x,p]~=~i\hbar$$
as a postulate of quantum mechanics? Or is it more correct to derive it given some form for $p$ in the ...
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2answers
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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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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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4answers
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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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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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A four-dimensional integral in Peskin & Schroeder
The following identity is used in Peskin & Schroeder's book Eq.(19.43), page 660:
...
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3answers
682 views
What is the significance of negative frequency in Fourier transform?
What is the significance of negative frequency in Fourier transform? Why we include the band widths of the negative frequency also while calculating band width of the signal.
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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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2answers
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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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What information is stored on gramaphones/tape recorders/CDs/DVDs
I'm a Software Developer by profession and my physics knowledge is limited what I had learned at high school level. Please excuse me if the question is trivial.
Question:
From what I know, a sound ...
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4answers
602 views
Intuitive explanation of why momentum is the Fourier transform variable of position?
Does anyone have a (semi-)intuitive explanation of why momentum is the Fourier transform variable of position?
(By semi-intuitive I mean, I already have intuition on Fourier transform between ...
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1answer
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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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2answers
347 views
“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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3answers
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Why use Fourier expansion in Quantum Field Theory?
I have just begun studying quantum field theory and am following the book by Peskin and Schroeder for that.
So while quantising the Klein Gordon field, we Fourier expand the field and then work only ...
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1answer
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Physical Significance of Fourier Transform and Uncertainty Relationships
What is the physical significance of a fourier transform?
I am interested in knowing exactly how it works when crossing over from momentum space to co ordinate space and also how we arrive at the ...
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Effect of a wavefront deformation on the far-field diffraction pattern of a TEM00
By performing Matlab simulations on a TEM00 mode (approximated by a gaussian intensity profile with a flat wavefront), I got the impression that applying wavefront deformations (such as a single ...
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1answer
69 views
Describing quantum intereference with only currents and densities
I know about and believe to understand the general wave equation based Kirchhoff diffraction formula, which in the Fraunhofer limit leads to a farfield complex wave function by Fourier transforming ...
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1answer
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Finding $\psi(x,t)$ for a free particle starting from a Gaussian wave profile $\psi(x)$
Consider a free-particle with a Gaussian wavefunction,
$$\psi(x)~=~\left(\frac{a}{\pi}\right)^{1/4}e^{-\frac12a x^2},$$
find $\psi(x,t)$.
The wavefunction is already normalized, so the next thing to ...
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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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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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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 ...
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3answers
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Acausality in solving time-domain inhomogeneous differential equations with Fourier transforms?
I was always wondering about the acausal nature of solutions obtained by Fourier transforms in the case of inhomogeneous equations. The solution usually revolves around the integration of the ...
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2answers
357 views
Field theory:functional derivative involving Fourier Transform
I have to solve the following functional derivative
$$
\frac{\delta}{\delta \Lambda(\mathbf{x})}\log[A-\mathbf{k}^2\Lambda(\mathbf{k})]
$$
where $\Lambda(\mathbf{k})$ is the Fourier transform of ...
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2answers
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The appearance of volume $V$ in the Fourier series representation of a periodic cubic system
In the textbook Understanding Molecular Simulation by Frenkel and Smit (Second Edition), the authors represent a function $f(\textbf{r})$ (which depends on the coordinates of a periodic system) as a ...
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1answer
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What would we never know in Physics if Fourier Transform were not discovered? [closed]
I am still unsure if Fourier Transform has any fundamental significance in Physics. Is it anything more than a calculation tool? For example sometimes people Fourier transform an equation to solve it ...
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1answer
220 views
Is there a relation between quantum theory and Fourier analysis?
These days I was studying the quantum theory.I found that some theories about that is similar to Fourier Transform theory.For instance, it says "A finite-time light's frequency can't be a certain ...
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3answers
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A question from Srednicki's QFT textbook
I have a question in Srednicki's QFT textbook.
In order to compute the vacuum to vacuum transition amplitude given by :
$$\left \langle 0|0 \right \rangle_{J}~=~\int \left [ d\varphi \right ]e^{i\int ...
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1answer
488 views
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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Measurement and uncertainty principle in QM
The Wikipedia says on the page for the uncertainty principle:
Mathematically, the uncertainty relation between position and momentum arises because the expressions of the wave function in the two ...
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2answers
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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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Difficulty in obtaining the Lorentzian lineshape for natural broadening [migrated]
Not sure if this maybe belongs more in the maths section, but since it comes from a physics problem i'll post here.
when calculating the natural broadening lineshape for a laser we have to take the ...
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Discrete sum over an exponential with imaginary argument, considering only every second lattice site?
Let's say I sum an exponential function $e^{\imath \left(k-k^{\prime}\right) x_{i}}$ over a chain system where every member of the chain is of the same type, e.g.,
A-A-A-...-A-A (total of N sites)
...
