A unitary linear operator which resolves a function on $\mathbb{R}^N$ into a linear superposition of "plane wave functions". Most often used in physics for calcalating the response of a time shift invariant linear system as the sum of its response to time harmonic excitation or for transforming a ...

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2answers
298 views

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 ...
3
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1answer
3k views

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 ...
6
votes
1answer
531 views

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 ...
2
votes
2answers
462 views

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 ...
4
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3answers
1k views

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: ...
6
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1answer
816 views

What is the meaning of the Fourier transform of Feynman propagator?

I know $K(a,b,t)$ is the probability amplitude that a particle that starts at point $a$ is found at point $b$ at a time $t$ later. There is also an expression that sometimes is called green function: ...
4
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3answers
467 views

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 ...
2
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1answer
716 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 ...
3
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2answers
463 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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2answers
360 views

Finding $\psi(x)$ from Fourier modes [closed]

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 } ...
6
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3answers
2k views

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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3answers
2k views

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 ...
3
votes
5answers
480 views

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 ...
3
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1answer
1k views

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 ...
28
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6answers
3k views

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 ...