Transform Definition and 1000 Threads

Hi everybody, can somewone tell me where am i wrong in this solution?(attached here) thank's

Question: Derive the relationship \int^t_{- \infty} f(\tau) d \tau \Leftrightarrow \frac{F(\omega)}{j \omega} + \pi F(0) \delta (\omega) (where \Leftrightarrow means "Fourier transforms into"). Attempt: I have already proved the relationship \frac{dg(t)}{dt} \Leftrightarrow j \omega G(...

Homework Statement I'm working on a long problem and have come to the final step. The answer seems so simple, but I can't quite get to it. I need to evaluate this integral: \int_0^{\infty}\ \left(e^{-k^2 t}/k\right)\sin(kx)\ dk Homework Equations Mathematica gives the result as...

What is the Fourier transform of $f'(ax)$, where a>0 is a constant? Firstly, I reasoned that (lets say $F[f]$ is the Fourier transform of f) $F[f('x)]=\frac{1}{a}F[f](\frac{k}{a})$ by scaling theorem, then using the derivative rule we get $F[f'(ax)]=\frac{ik}{a}F[f(x)](\frac{k}{a})$. But when I...

Ohno Potential is modeled by v(r)=\frac{U}{\alpha ^{2}r^{2}+1}. U and \alpha are constants. I try to Fourier transform it V(q)=\int V(r) e^{iqr\cos \theta}r^{2} \sin \theta d \phi d \theta dr It gives V(q) = 2 \pi U \int \frac {r \sin qr}{\sqrt{\alpha ^{2} r^{2}+1}} dr The...

I'm new to Laplace and having slight difficulty with what looks like an obvious equation. I can do basic first and second order equations. Why is it that the seemingly easy equations are always the ones to stump you? Homework Statement \frac{dy}{dx}=-y y=2, x=0, y_{0}=2 Homework...

Homework Statement Two identical circuits are cascaded, without the second circuit having any loading effect on the first circuit. If the laplace transform of the impulse response of the cascade is 4/(s+1)^2. a)determine the impulse response of each circuit alone as a function of time. b)if...

I have a question that has stumped me a bit, i am not sure how to use the definition to calculate it, i can use the tables, but i don't think that's what is needed. Using the definition of the Laplace transform, determine the Laplace transform of I can do it with the table but i am not sure...

Hi. Homework Statement \int\limits_0^{ + \infty } {\frac{{dt}}{{{e^{st}} \cdot (1 + {e^t})}}} Homework Equations The same as... Laplace\left[ {\frac{1}{{1 + {e^t}}}} \right] The Attempt at a Solution Found no elegant properties related to Laplace transform here. So figured my...

Homework Statement a) Find the normalization constant N for the Gaussian wave packet \psi (x) = N e^{\frac{-(x-x_{0})^{2}}{2K^{2}}}. b) Find the Fourier Transform and verify it is normalized. 2. The attempt at a solution a) I think I've got \psi (x) = N e^{\frac{-(x-x_{0})^{2}}{2K^{2}}} \int...

Hi everyone, I have a question on the discrete Fourier transform. I already know its a change of basis operator on C^N between the usual orthonormal basis and the "Fourier" basis, which are vectors consisting of powers of the N roots of unity. But if i recall correctly from complex...

Hi, I am currently confused about something I've run across in the literature. Given that \nabla^2\phi = \phi_{xx}+\phi_{zz} = 0 for z\in (-\infty, 0] and \phi_z = \frac{\partial}{\partial x} |A|^2 at z=0. for A= a(x)e^{i \theta(x)} . The author claims that...

I'm trying to find \frac{1}{2\pi}\int \limits_{-\infty}^{\infty}e^{-itx}\frac{1}{a^2+x^2}\mathrm{d}x where 'a' is a constant. First I noticed that there is \frac {\partial \arctan x}{\partial x} in this and using a substitute got \int \limits_0^{\pi / 2}\cos( t \tan x )\mathrm{d}x with some...

So I've been searching on the internet and in my textbook and I can't find a simple enough explanation of the Laplace transform of a product of functions. Is it absolutely necessary to evaluate the integral using different methods or is there an easier way?

Homework Statement Consider the following initial value problem: y''-6y'-7y=sin(9t) y(0)=-4, y'(0)=-3 I need to solve for L[y(t)]Homework Equations The Attempt at a Solution Here are the steps I've taken to solve it: L(y'')-6L(y')-7L(y)=L(sin(9t))...

Homework Statement Hi all, I'm struggling to find the Inverse Laplace transform of the following function: F(s) = (1+ 4e(-s) - 5e(-3s)) / s(s2 + 11s + 55), where F(s) is a Laplace transform Solution should be in terms of complex exponentials and unit step functions. Homework EquationsThe...

Hi all, I'm struggling to find the inverse Laplace transform of the following function: F(s) = (1+ 4exp(-s) - 5exp(-3s)) / s(s^2 + 11s + 55)Any help is appreciated. Thanks

Hi, I recently posted another question about a Laplace transform and now have a question about taking the inverse Laplace transform. Again, my professor did not cover this topic as well as I could have hoped for, and so I am stuck on this problem as well. Again, I understand the idea of Laplace...

Hi, I've been asked to find the Laplace transform of a function and I have not the slightest clue where to begin. My professor derived the basic Laplace transforms in class(sin, cos, delta function, step function, etc), all of which I understood perfectly. However, he never really gave us an...

Homework Statement f(t)=t*e^(-2t^2) Find the Fourier Transform F(w) of f(t). It is given that when f(t)=e^[(-at^2)/2] F(w)=√(2*pi/a)*e^[(-w^2)/2a] Homework Equations The Attempt at a Solution The transform of e^(-2t^2) is easily obtained from the given information, and I got...

Homework Statement y'' + w^2y = cos(t) y(0) = 1 y'(0) = 0 w^2 not equal to 4 Homework Equations Laplace integral, transform via table/memory... Y(s) = F(s) or whatever you like to use The Attempt at a Solution s^2Y(s) - sy(0) - y'(0) + w^2Y(s) = s/(s^2 + 1). Right side is...

Homework Statement Solve the differential equation using laplace transforms. Assume zero intial conditions and that the forcing functions are zero prior to t=0 x''(t) + 6x'(t) +8x(t)=sin3t Homework Equations The Attempt at a Solution I took the laplace transform which I found to be after...

Hello, I'am looking for de correct transformation formule:\mathcal{L}[f(t).g'(t)] (and proof). I'am not looking for method to solve it by means of integrating g'(t), offcourse this a possible way. But assume that g(t) is much work to calculate. So is there a good one to one formule...

Say you find the laplace transform V(s) and want to switch it back to the time domain, once you've done this, how do you determine which parts of the total solution correspond to the complementary solution and particular solution respectively? Do you just find which parts approach zero as time...

Hello Everyone, Actually my question is related to Window Fourier transform (WFT). I have studied that with the help of WFT we can easily determine the phase of the image. Like by multiplying the window to only a specific part of the input and considering the outside part of the window equals...

Homework Statement Just something I am working through and am a bit stuck on. Homework Equations I have taken the Fourier transform of an RC circuit which gives me : Y(ω)=((X(ω))/(1+iωτ)) If i take the voltage across the circuit as white noise then i get: Y(ω)=σ^²/2π/(1+iωτ)) How...

\geqHomework Statement Find the Fourier Transform of y = exp(^{}-at)sin(\omega_{}0t) for t ≥ 0 and = 0 for t < 0 Find the amplitudes C(\omega, S(\omega), and energy spectrum \Phi' for \omega > 0 if the term that peaks at negative frequency can be disregarded for pos frequency...

I haven't had differential equations yet, so I am struggling in your math methods class. I understand what a Fourier Transform is, but I'm having trouble with this particular problem. Homework Statement Here's a screenshot. Better than I can write it. http://i.imgur.com/PQ6tB.png The...

I'm confused about the DFT of the data, fn = cos(3\pin/N) for n=0,1,...,N. It is definitely an even function, and I read that the Fourier coefficients of an even function is real. But when I take the FFT of this in Matlab I get complex numbers, not real numbers. What am I missing? Thanks ...

Hi, I am trying to derive one transfer function for a system, but got stuck at a point. I want the solution to the ratio V_o(s)/V_g(s), the transfer function. V_o(s) = [a*L{(V_g)^2} - b*L{V_o * (V_g)^2} - c*V_g(s) - d/s]*z(s) In the following equation, I have: s-> lapace transform...

Heat Equation (Non Homogeneous BCs) - Difficult Laplace Transform... help! ;) Hi I'm trying to model the temperature profile of an inertia friction welding during and after welding. I have the welding outputs and have come up with a net heat flow wrt time during the process. I now want to...

Homework Statement Determine the Laplace transform: g(t) = 2*e^{-4t}u(t-1) The Attempt at a Solution Essentially we're told for a time shift we multiply the Laplace transform pair of the function (without the delay) by e^{-as} So here a = 1 (for the delay) The Laplace transform for e^{-4t}...

Hello all, I want to extract the period out of a complex discrete signal. Currently I have the Matlabscript of the attachement. However, the values I get out of this script are not correct. There is some kind of systematic bias in it. I think it has something to do with index *...

How you get Fourier transform from Fourier series? Do Fourier series becomes Fourier transform as L --> infinity? http://mathworld.wolfram.com/FourierTransform.html I don't understand where discrete A sub n becomes continuous F(k)dk ( where F(k) is exactly like A sub n in Fourier series)...

I'm attempting to find the inverse laplace transform of \frac{25}{(1-s)^2*(4+s^2)} I get to this point but can't get the values of A B and C when equating coefficients. 25/(s-1)=A(4+s^2)+(Bs+C)(s-1) Also for a separate question: (s+1)/(5-4s+s^2) How do you find the inverse...

I have a time series data, I want to use wavelet transform to de-noise the data and then use neural network to analysis the transform data. However, I quite not understand about the wavelet transform. Can tell me about how to use wavelet transform? How to determine the scale? Is it suitable use...

Homework Statement I've attached the multiple choice question Homework Equations The Attempt at a Solution I inversed laplaced the problem and i get an answer of 3 H(t-3) sin(9(t-3)) which isn't any of the options so I chose F but that was wrong. So far I've confidentally...

Hi Do Fourier Transforms give us actual amplitude/phase of the particular frequency (ejωt) just like Fourier series? Thanks Salil

Homework Statement Having found the laplace transform of a differential equation. I must now find X(t). All of my work is attached. The problem I am having is fitting my function of s to my table of transforms. I tried using partial fractions but it took me in a loop.The Attempt at a Solution...

Homework Statement Hey guys, I've attached the question that's troubling me. I've also attached the table and formulas of Laplace transform for you convenience. Homework Equations attached The Attempt at a Solution Right now, I am thinking the best way to do this problem is...

Homework Statement We have been given a table of laplace transforms and have been asked to show them using the definition. ∫0∞e-stf(t)dt. But this one I have no clue where to begin ∫0tf(t)dt the laplace transform of this is F(s)/s. Can anyone tell me what to do with this one? Thank you...

I'm taking the Fourier transform of a signal. This integral has bounds from -∞ to ∞, but since the signal is 0 for negative t, the bounds become 0 to ∞ doing the integration, the antiderivative I get is et*(-3-jω+2j) where j is sqrt(-1) Now I have to evaluate this at t=infinity (since it is a...

Homework Statement Could someone please explain this to me? I have read several notes on it, but do not really follow the reasoning: The Attempt at a Solution When t = 0, -1/s*e^-st = -1/s because e^0 = 1. When t goes to infinity is the part I do not fully understand. Why...

I need to use the Fourier transform to solve the wave equation: $\begin{aligned} & {{u}_{tt}}={{c}^{2}}{{u}_{xx}},\text{ }x\in \mathbb{R},\text{ }t>0, \\ & u(x,0)=f(x), \\ & {{u}_{t}}(x,0)=g(x). \end{aligned} $ So I have $\dfrac{{{\partial }^{2}}F(u)}{\partial...

Homework Statement So this is a physics problem, but this question doesn't really have to do with the "physics" part of it as much as simply calculating the Fourier transform. (This is a second year physics course and our prof is trying to briefly teach us math tools like this in learning...

Given $\begin{aligned} & {{u}_{t}}={{u}_{xx}},\text{ }x>0,\text{ }t>0 \\ & u(x,0)={{u}_{0}}, \\ & {{u}_{x}}(0,t)=u(0,t). \end{aligned} $ I need to apply the Laplace transform to solve it. I'll denote $u(x,s)=\mathcal L(u(x,\cdot))(s),$ so for the first line I have $s\cdot...

Homework Statement Homework Equations The Attempt at a Solution We went over the Laplace transformation today in my DE course. We only covered essentially, "how to do it", so: L(f(t)) = \int_{0}^{\infty}f(t)e^{-st}dt (also, how do you make the fancy f and curly brackets in Latex?)...

Hi everyone, I have a problem with finding the transfer function of a linear system. It happens that in some terms the input and the output are multiplying and I have no idea how to do the Laplace transform of this. The system is a car and I am only studying its speed. The input is the...

Hello all, first time here and I have really silly problem... I am working on something in MATLAB, in which I have to make discrete Fourier transform of gaussian distributed variable. i.e. array of numbers which are taken from f(x)~exp(-x^2). I know that when you Fourier transform it with...

Hello, I'm looking at some sporting data (similar to goals in a match) and trying to figure out what distribution applies to their count per match. Typically, Poisson is used in the industry to model the distribution. When I look at the historical events, poisson isn't too bad, but tends...