# Tagged Questions

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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### 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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### 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 $g(k)$: $$\int |f(x)|^2 dx=\int|g(k)|^2 dk$$ has the ...
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### 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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### Quantization of a free field: Klein-Gordon case

I am a beginner and reading this course text on QFT. The author first introduces the KG equation: $$\partial_\mu\partial^{\mu}\phi+m^2\phi=0$$ [with Minkowski signature $(+,-,-,-)$]. Then the ...
Figure 1.(c) shows the Test image reconstructed from MAGNITUDE spectrum only. We can say that the intensity values of LOW frequency pixels are comparatively more than HIGH frequency pixels. $$f(x,y)=... 2answers 511 views ### Inverse Fourier Transform Of K-space Image…what is the object space scale? Checked around a buch and could not find any help. But I needed help with: Understanding that if I get the Inverse FT of K-space data, what is the scaling on the X-space (object space) resultant ... 2answers 620 views ### Effect of a wavefront deformation on the far-field diffraction pattern of a TEM00 By performing Matlab simulations on a TEM00 mode (approximated by a gaussian intensity profile with a flat wavefront), I got the impression that applying wavefront deformations (such as a single ... 2answers 341 views ### Massless boson in 2D and its (retarded) propagator I have the retarded propagator for a free scalar field in 1+1 dimensions. Inside the light cone, this looks like J_0(m \sqrt(t^2-x^2)), J being a Bessel function. When I take the massless limit, ... 1answer 109 views ### Light, Fourier Transforms, Spherical Harmonics Mathematically, I'm having trouble understanding where we can use what with light. I read somewhere on this site that Huygen's Principle is effectively just taking an expansion of a wave onto the ... 1answer 261 views ### Getting an equivalent integral equation from a given one I'm reading a paper and don't understand some of the calculations. We are given an integral equation with asymptotic boundary conditions \rho_+(u)=\frac{1}{2\pi} \int\limits_{|v|>\mu}^{}\mathrm{d}... 1answer 772 views ### Fourier transformation, electric field and magnetic field to have a shielding lattice against particles With Fourier-Series Expansion, we can write a function as sum of many non-repating different frequncied different amplituded sine and cosine functions. Lets assume we know electric-field and magnetic-... 0answers 64 views ### Interpreting the Fourier transform of a Gibbs measure Recall that a Gibbs measure gives a probability distribution on states x of the form$$ p_X(x) = \frac{1}{Z(\beta)}\exp(-\beta E(x)) $$As I understand, the function E is interpreted as the ... 1answer 220 views ### Diffraction and k-space Regarding diffraction I am a little bit lost reading about reciprocal space and the space of k's. As I understand it the Fourier relationship between a wavepacket \Psi(\vec r,t) and the complex ... 0answers 101 views ### Non-Hermiticity when Fourier transforming onto a finite lattice I'm doing numerical simulations. I have the Haldane model in a honeycomb lattice where$$ H = \sum \limits_{<ij>}a^\dagger_i b_j + h.c $$Where i belongs to sublattice A, and j to ... 5answers 512 views ### Does this statement make any sense? I am asking this question completely out of curiosity. The other day, my roommate, by mistake, used 'Light year' as a unit of time instead of distance. When I corrected him (pedantic, much), he said ... 5answers 12k views ### Why are AC quantities represented by sine waves always? Usually we use a sinusoidal wave form to represent a alternating quantity. Why not a cosinusoidal wave or a ramp wave form? In sine wave forms we can indicate the maximum and minimum amplitude and ... 2answers 309 views ### Why higher frequencies in Fourier series are more suppressed than lower frequencies? One can expand any periodic function in sines and cosines. When calculating the coefficients a_0, a_n, and b_n one find that a_1>a_2>...>a_n>..., similarly for b_n. Is there an ... 3answers 463 views ### What information is stored on gramaphones/tape recorders/CDs/DVDs I'm a Software Developer by profession and my physics knowledge is limited what I had learned at high school level. Please excuse me if the question is trivial. Question: From what I know, a sound ... 4answers 91 views ### Convolution Theorem in Physics I'm getting ready for my classes to start next semester in Grad school, and I'm reading over Fourier Transforms and their applications. I came across the Convolution Theorem, namely, that if we have a ... 3answers 135 views ### How can F_0\cos\omega t change to F_0e^{i\omega t} in driven oscillator equation? I have one thing that confuses me on deriving the solution for the Linear Forced Oscillator. Suppose we have the equation as$$ma + rv + kx = F_0 \cos \omega t$$What confuses me is when the driving ... 3answers 2k views ### How do human ears distinguish the frequencies in sound? If they do a Fourier transform, how can they know the formula to find coefficients? 3answers 285 views ### How to measure an image's contrast? I'm studying Fourier optics and Interferometry and I intend to determine the contrast of an image using computer software. My teacher of Experimental Physics didn't tell me how to do it, and so, I'm ... 3answers 336 views ### Fourier Transforms Related to Green's Functions I'm reading a text on field theory where there are a number of assertions made about Fourier transforms that I'm finding confusing. For example, let G^R = -i \theta(t - t')e^{-i \omega_0 (t - t')}. ... 2answers 331 views ### What is the significance of the Fourier coefficients? Let us take an example, a white ray (which is composed of bunch of frequency components) is passed through a prism, the ray gets split (decomposed) into its elementary vibgyor colours (i.e.different ... 3answers 61 views ### Why is response of system same frequency as driving force frequency Super basic question: why does a system (to be definite, perhaps assume a collection of coupled harmonic oscillators) respond (in the steady-state, after transient effects have dissipated) with all ... 2answers 345 views ### Is a wave packet physically realizable as a Fourier series? In QM a wave packet is modeled as an infinite, or almost infinite, Fourier series, and the Fourier transform provides a transformation between momentum space and position space. To what extent is ... 3answers 412 views ### Why does \nabla \to ik when you Fourier transform? I am reading a text that describes the scattering of light by a particle with dielectric constant \epsilon After a bit of maths starting from Maxwell's equations they obtain:$$\nabla (\nabla \...
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 \$\...