# Questions tagged [fourier-transform]

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 calculating the response of a time shift invariant linear system as the sum of its response to time harmonic excitation or for transforming a quantum state in position co-ordinates into one in momentum co-ordinates and contrawise. There is also a discrete, fast Fourier transform for discretised data.

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### Complex fourier transformation function [duplicate]

can the FT function can be a complex function ? and if yes what does it mean because in all cases i came across till now the FT function only had a real part
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### Meaning of complex Fourier transformation function

what does it mean, if the Fourier transformation function of an electromagnetic wave is complex? I know that normally the FT function $f(k)$ shows the wavenumbers that are involved in the wave. but i ...
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### Fourier Transform of a short signal

if I have a sine wave signal for a duration of only a few seconds, the Fourier transform will show me, that this signal corresponds to a range of frequencies. Why is this the case? I do understand ...
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### Determining Characteristics of Spatial Light Modulator (SLM)

im quite lost somehow. I know this is a really basic thing and I know I should be able to do it, but something is going on with me and I tend to have problems with everything these days. Anyway: I ...
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### Asymptotic form of a Coulomb-like integral

I need to evaluate or work out the asymptotic scaling of the following integral: \begin{equation} I~=~\int_{\mathbb{R}^3} dq d^2p \frac{e^{i\vec{p}\cdot \vec{r}}e^{iq z}}{p^2 + \frac{1}{g^2}q^4} \end{...
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### Propagators in position space

What are the possible applications of position-space representations of propagators? I'm speaking not only of the well-known free field case, but also of the particles in external fields and/or curved ...
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### What is the meaning of the absolute of the Fourier transform in this context?

In a course talking about Fourrier transform and Nyquist frequency, there is this sentence that I can't understand: "If a signal has $|F(w)| \geq 0$ only for frequencies till f, than such ...
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### Dualities in Physics and Fourier Transforms

In many articles, authors compare physical dualities to Fourier transforms. For example: Joseph Polchinski, in his article "String Duality" (hep-th/9607050v2), writes: "Weak/strong ...
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### What is the one-sided Fourier transform of a constant? [migrated]

A definition of the Fourier transform commonly used is (I always forget which convention of normalization to use) \begin{align}f(\omega)=\int_{-\infty}^\infty e^{i \omega t}f(t) dt\end{align} For a ...
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### A Problem on Tunneling in a dissipative environment

I am currently self-studying Many-Body Physics and I am using the textbook Condensed Matter Field Theory . I am currently trying to figure out the problem on page 151 (Chapter 3 and problem called &...
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### Fourier transform of the state?

I'm trying to make sense of the following equation I saw on Wikipedia: https://en.wikipedia.org/wiki/Momentum_operator#Fourier_transform I saw on wikipedia that \begin{equation} \langle\psi|\hat{p}|\...
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### How do I calculate the inverse Fourier transform of the delta function? [migrated]

In the context of single-pixel imaging, the following statement is given: "A Fourier basis pattern $P_F (x,y)$ can be obtained by applying an inverse Fourier transform $\delta_F (u, v, \phi)$to ...
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### How does a transformation domain differ from a spatial domain?

In the context of single-pixel imaging, the following statement is given: "Global transformation has a property that each point (coefficient) in the transformation domain is a weighted sum of all ...
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### Why won't sampling at time intervals shorter than the detector's response provide new information?

"When Fourier analysing a signal, sampling at time intervals shorter than the detector's response won't provide any new information, only smoother data." This was told to me, but I don't ...
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### Fourier transform of sine function

While solving the Fourier transformation of a sine wave (say $h(t)=A\sin (2 \pi f_0 t)$) in time domain, we get two peaks in frequency domain in frequency space with a factor of $(A/2)j$ with ...
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### Confusion about modes and quantum field theory

I'm learning quantum field theory from P&S and Srednicki. I'm having a lot of difficulties understanding the concept of a momentum state. In particular, I'm confused about how to interpret the ...
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### Can the sound of infinitely long played music be decomposed in sine (or cosine) forms?

Every arbitrary waveform (except non-linear ones) can be decomposed in sine (or cosine) waveforms that spatially extend to infinity. That is if the waveform has a finite spatial extent. But say that I ...
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### Accounts on the solutions of the Dirac equation

Consider the Dirac equation $(i\gamma^{\mu}\partial_{\mu}-m)\psi = 0$. As it is well known, there are different representations for the matrices $\gamma^{\mu}$, $\mu = 0,1,2,3$, the most famous ones ...
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### Convert gaussian function from 3D configuration space into 3D momentum space

I know, If we convert a gaussian function from 1D position space into 1D momentum space, it will be again a gaussian function. But if we have a gaussian function in a 3D position space, how it will be ...
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### White light interferometer

I am building white-light Michaelson interferometer and I am registering interference in frequency domain via spectrometer. I read an article, where the same is done (just Mach-Zender interferometer) ...
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### Interference fringes movement analysis

I am registering interference fringes on CCD linear sensor from Michelson inteferometer runned by He-Ne laser. I am sampling every 15-20 ms. I made a program to follow fringe movement and to track ...
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### Leakage of superconducting qubit: why it occurs with short driving pulses and not as well with long ones

My question in very short: Short pulses on superconducting qubit usually induce leakage. But a long pulse can be seen as a sequence of short pulses (imagine all of the short pulse as square pulses: ...