Transform Definition and 1000 Threads

Hi, My aim is to get a series of images in 2D space that run over different timestamps and put them through a 3D Fourier Transform. So my 3D FT has 2 spatial axes and one temporal axis. However I have never done anything like this before, and I have a very basic knowledge of Python. So...

Firstly, if this is an inappropriate forum for this thread, feel free to move it. This is a calculus-y equation related to differential equations, but I don't believe it's strictly a differential equation. The question I'm asking is which functions...

Homework Statement OK, we're given to practice Fourier transforms. We are given f(x) = \int^{+\infty}_{-\infty} g(k) e^{ikx}dk and told to get a Fourier transform of the following, and find g(k): f(x) = e^{-ax^2} and f(x) = e^{-ax^2-bx} Homework Equations The Attempt at a Solution For...

Homework Statement Hi. I need help to resolve the inverse laplace transform of {1/((x^2)+1)^2}2. The attempt at a solution I have tried to do: {(1/((x^2)+1) * (1/((x^2)+1)} then, convolution, sen x But, isn't working Thanks for your help :)

Is there a time domain function whose Fourier transform is the Dirac delta with no harmonics? I.e. a single frequency impulse

Hello. I'm wondering if anyone has a table of transforms showing the result of an Abel transform on a Gaussian distribution. I have been unable to find the solution to this. Many thanks for any help. I'm reconstructing an an image from a picture that fits a Gaussian very well, hence I'm hoping...

I have this expression: f(\tau) = 4 \pi \int \omega ^2 P_2[\cos (\omega \tau)] P(\omega) \, \mathrm{d}w \quad [1] where P_2 is a second order Legendre polynomial, and P(\omega) is some distribution function. Now I am told that, given a data set of f(\tau), I can solve for P(\omega) by either...

A first stage of the determination. We have a body of length L = AB, which moves along the x-axis with velocity v, say that coming to us. A -------- B v <--- | | h - vertical distance | ./ - a light converges to us with the speed eq. c | / O ---------> x At some time t = 0, we see the point A...

Hi All, I'm playing around with an arduino, and have build a PID controller that controls the temperature of a light bulb, measured with an NTC. All is working fine I'm looking to get a bit more theoretical on the subject and have modeled the system in a simulink like environment. I want...

Basically I am trying to lorentz transform the magnetic field along θ of a bunch particles which have a gaussian distribution to the radial electric field. However the magnetic field in θ is dependent on the longitiudinal distribution. Now initially i thought we would just use the standard LT...

Hi! I'm trying to show that the differential from equation $$D \star F = 0$$ transform homogeneously under the adjoint action ##F \mapsto gFg^{-1}## of the lie group ##G##, where ##D## denotes the covariant exterior derivative ##D\alpha = d \alpha + A \wedge \alpha## for some lie algebra valued...

When I sample a certain digital signal with increasing sampling frequency, the fast Fourier transform of the sampled signal becomes finer and finer. (the image follows) Previously I thought higher sampling frequency makes the sampled signal more similar to the original one, so the Fourier...

Homework Statement Ds + E / (s^2 +1)^2 Homework Equations The Attempt at a Solution Ds / (s^2 +1) + E / (s^2 +1) D[s/(s^2 + 1)^2] + E [1 / (s^2 + 1)^2]

before I go to bed(it's 11:30pm in my place), here is the last problem that I need help with find the inverse Laplace Transform $\frac{4s-2}{s^2-6s+18}$ the denominator is a non-factorable quadratic. I don't know what to do. thanks!

find the inverse Laplace of the ff: 1. $\frac{n\pi L}{L^2s^2+n^2 \pi^{2}}$ 2. $\frac{18s-12}{9s^2-1}$ for the 2nd prob I did partial fractions $\frac{18s-12}{9s^2-1}=\frac{9}{3s+1}-\frac{3}{3s-1}$ $\mathscr{L}^{-1}\{\frac{18s-12}{9s^2-1}\} =...

$\mathscr{L}\{\sin^{2}4t\}$ $\mathscr{L}\{\sin(3t-\frac{1}{2}\}$for the 2nd prob here's what I have tried $\mathscr{L}\{\sin(3t)\cos(0.5)-\cos(3t)\sin(0.5)}$ $\cos(0.5)\mathscr{L}\{\sin(3t)\}-\sin(0.5) \mathscr{L}\{\cos(3t)\}$ $\frac{3\cos(0.5)-s\sin(0.5)}{s^2+9}$ ---> is this correct? for...

please help me solve this problem $\mathscr{L}\{e^{3a-2bt}\}$ here's my attempt $\mathscr{L}\{e^{3a}\cdot e^{-2bt}\}$ from here I couldn't continue I looked up my table of transform but nothing matches the problem above. I'm not sure if the first shift formula would work here. please help...

To calculate the DOS of a material, the electronic structure typically needs to be calculated first. This requires lots of expertise and the accuracy is questionable. I'm interested in seeing if there's some shortcut to get some general properties of the DOS: If I could arbitrarily deform...

As it can be read here, http://en.wikipedia.org/wiki/Laplace_transform#Relation_to_power_series the Laplace transform is a continuous analog of a power series in which the discrete parameter n is replaced by the continuous parameter t, and x is replaced by exp(-s). Therefore, computing a...

Hi All, I have a problem I've been thinking about for a while, but I haven't come up with a really satisfactory solution: I want to do a discrete Fourier transform on data that has been sampled at 2 different sampling frequencies. I've attached a picture of what my data will look like...

Homework Statement Find the FT of the following signal The function is: f(t) = t(\frac{sen(t)}{t\pi})^2 Homework Equations Fourier transform: F(\omega)= \int_{-\infty}^\infty f(t)e^{-jt\omega} My attempt began with this Fourier transform, and that's my goal: F[tf(t)]=...

I was wondering if anyone could help me with this integral. I've heard of contour integration but I'm unsure of how it would be used for this integral.

1. Hi! I am new at this forum, and english is not my native language, so, I hope I can make myself clear. A teacher send us a list of activities, but he did not give us the theory about it (the theoretical class). So, I have read a few things on the internet and I have solved some exercises. I...

Hello, I am searching for the Laplace transform of this function u_a(y)\frac{\partial c(t)}{\partial t} where u_a(y) is the Heaviside step function (a>0). Can anyone help me? Thanks in advance! Paolo

Homework Statement \int_{-\infty}^{\infty} |k|^{2\lambda} e^{ikx} dkHomework Equations The Attempt at a Solution As you can guess, this is the inverse Fourier transform of |k|^{2\lambda}. I've tried splitting it from -infinity to 0 and 0 to infinity. I've tried noting that |k| is even, cos is...

Homework Statement ƒ(t) = 1.15t Homework Equations Standard Laplace Transform Table The Attempt at a Solution L(f(t)) = e(t * ln(1.15) = 1 / (s - ln(1.15))

For two-body decay, in the center of mass frame, final particle distribution is, $$ W^*(\cos\theta^*,\phi^*) = \frac{1}{4\pi}(1+\alpha\cos\theta^*) $$ We have the normalization relation , ##\int W^*(\cos\theta^*,\phi^*)d\cos\theta^* d\phi^*=1##. And we also know that in CM frame ##p^*##...

I have a third order derivative of a variable, say U, which is a function of both space and time. du/dx * du/dx * du/dt or (d^3(U)/(dt*dx^2)) The Fourier transform of du/dx is simply ik*F(u) where F(u) is the Fourier transform of u. The Fourier transform of d^2(u)/(dx^2) is simply...

We have a wave ψ(x,z,t). At t = 0 we can assume the wave to have the solution (and shape) ψ = Q*exp[-i(kx)] where k = wavenumber, i = complex number The property for a Fourier transform of a time shift (t-τ) is FT[f(t-τ)] = f(ω)*exp[-i(ωτ)] Now, assume ψ(x,z,t) is shifted in time...

Can anybody help in in finding the Fourier transform of f(x) = xe^-x where -1<x<0 and f(x)= 0 otherwise?

Magic of Fourier Transform? Hello everyone,i am doing my project in image processing... i have done video sementation using the Fourier transform . I applied 3-D fft on video frames ((gray image(2D)+no of video frames(1D)=3D) and Obtained magnitude and phase spectrum and reconstructed video...

Homework Statement f(p) is the Fourier transform of f(x). Show that the Fourier Transform of eipox f(x) is f(p- p0).Homework Equations I'm using these versions of the Fourier transform: f(x)=1/√(2π)∫eixpf(p)dx f(p)=1/√(2π)∫e-ixpf(x)dx The Attempt at a Solution I have...

2D Fourier Transform on a non-rectangular area Is it possible to perform a Fourier transform on a shape instead of a rectangular region? To be specific I am attempting to make a linear zoom function that doesn't produce any pixelation and that mimics natural blur that occurs with distance...

hey pf! physically, what does a Fourier transform do? physically what comes out if i put velocity in? thanks! josh

calculate the Fourier transform of the function g(x) if g(x) = 0 for x<0 and g(x) = ##e^{-x}## otherwise. putting g(x) into the transform we have: ##\tilde{g}(p) \propto \int_{0}^{inf} e^{-ipx} e^{-x} dx## which we can write: ##\tilde{g}(p) \propto \int_{0}^{inf} e^{-x(ip+1)} dx##...

Fourier transform of density matrix of cos(x+y)*cos(x-y) I would like to know whether there exists a solution to the following integral, \frac{1}{\pi} \int\limits_{-\infty}^{\infty} \cos(x+y)^\alpha \cos(x-y)^\alpha e^{2ipy} The above expression is the Fourier transform of the...

I am sure this is not the best description of the problem, so let me know how I can clarify. Say there are 2 coordinate systems, with one orbiting around the other. Call one fixed ƒ and the other rotating ρ. The goal is to find the transform between the two frames. What's known is 1) A...

Hi all, Now naturally after completing a physics degree I am very familiar with the form and function of the Fourier Transform (FT) but never have grasped it quite conceptually. I understand that given a function f(x) I can express every functional value as a linear combination of complex...

I usually see that Laplace transform is used a lot in circuit analysis. I am wondering why can we know for sure that the Laplace and its inverse transform always exists in these cases. Thank you.

y′′+4y′+4y=f(t) where f(t)=cos(ωt) if 0<t<π and f(t)=0 if t>π? The initial conditions are y(0) = 0 , y'(0) = 1 I know that f(t)=cos(ωt)−uπ(t)cos(ωt), the heaviside equation. AND ω is allowed to vary, supposed to find the general solution, i.e. f(t) in terms of ω I think that after...

Use Laplace transfer to find the solution of the following initial value problem: y''+4y'+4y=f(t) where f(t) = cos(ωt) if 0<t<π and f(t)=0 if t>π ? Also, y(0) = 0, y'(0) = 1 Currently, I have gotten to here, but not sure how to perform inverse Laplace: (s+2)² * F(s) − 1 = [s/(s²+w²)]...

Homework Statement I had a question in my midterm, it was to find inverse laplace tansform of: (4s+5) / (s^2 + 5s + 18.5) Where ^ denotes power. Homework Equations The Attempt at a Solution My answer was to find the complex roots of equation (s^2 + 5s + 18.5) , by them...

In all the literature that I have seen it is mentioned that these two are "branches" of integral geometry, but no where I can see the exact connection since one is connected with probability and the other is an integral. I have seen this, but it is not clear...

Suppose I have a function of the type: h(t) = g(t)f(t) where g(t) is a periodic function. Are there any nice properties relating to the Fourier transform of such a product? Edit: If not then what about if g(t) is taken as the complex exponential?

I have a set of differential equations with the basic form: dy_n/dt = t*(a_(n-1)*y_(n-1)+b(n+1)*y_(n+1)-2c_n*y_n) So the time depence is a simple factor in front of the coefficient matrix. Does this set of differential equations have closed form solutions?

Which is the difference between the Fourier integral and Fourier transform? Or they are the same thing!? Fourier integral:

Homework Statement d^2x/dt^2 - 3 dx/dt + 2x= 2e^3t give that at t=0, x=5, and dx/dt=7 Homework Equations i can't figure out how to derive the values of A, B, and C from the attempted equation solution. please help me out here. thanks The Attempt at a Solution

I'm out of college and am brushing up on Laplace Transforms. I have a problem I've solved, but I believe the solution I got is wrong and can't find my error. The problem is 2x''-x'=t*sin(t) x(0)=5,x'(0)=3 My solution... Take the Laplace Transform 2(s^2x-5s-3)-(sx-5)=2s/(s^2+1)^2...

Homework Statement Find possible momentum, and their probabilities. Find possible energies, and their probabilities. Homework Equations The Attempt at a Solution First, we need to Fourier transform it into momentum space: \psi_k = \frac{1}{\sqrt{2\pi}} \int \psi_x e^{-ikx} dx =...

Homework Statement Let FT(f) = Fourier transform of f, (f*g)(x) = convolution of f and g. Given FT(f*g) = FT(f)FT(g), the first part of the convolution theorem, show that FT[fg] = [FT(f)*FT(g)]/2pi. Homework Equations Duality: FT2f(x) = (2pi)f(-x) Convolution: (f*g)(x) =...