Transform Definition and 1000 Threads

Homework Statement Ok I know Fourier transform pair for u(t) is pi*del(w)+1/(j*w) Am I right to say the transform pair of u(t)-u(t-1) is [pi*del(w)+1/(j*w)]-[pi*del(w-1)+1/(j*(w-1)] If not what is it? thanks

On MHF... Integral Caculation ... the user widapol did have some difficulties in the computation of the integral... $\displaystyle \int_{0}^{\infty} \ln^{2} (1+t)\ e^{- s t}\ dt$ (1) ... which of course is the L-Transform of the function $\displaystyle \ln^{2} (1+t)$. Remembering thye basic...

Say you have some function that is periodic in a parameter k. The discrete Fourier transform from a sampling may be found in the usual way, giving the frequency spectrum in k. But what if I want to find the frequency spectrum in 1/k ? I'm not really sure what this is called, and so I've had a...

Homework Statement Hi guys! I'm basically stuck at "starting" (ouch!) on the following problem: Using the integral representation of the Bessel function J_0 (x)=\frac{1}{\pi} \int _0 ^\pi \cos ( x\sin \theta ) d \theta, find its Laplace transform. Homework Equations \mathbb{L}...

Homework Statement I'm trying to Solve for an impulse response h(t) Given the excitation signal x(t) and the output signal y(t) x(t) = 4rect(t/2) y(t) = 10[(1-e-(t+1))u(t+1) - (1-e-(t-1))u(t-1)] h(t) = ? y(t) = h(t)*x(t) --> '*' meaning convolution! I am unsure how to take the Fourier...

Homework Statement I must calculate the Laplace transform of the following function: f(x)=1 for x \in [0,1] \cap [2,3] \cap [4,5] \cap ... , f(x)=0 otherwise. Homework Equations The Laplace transform is \mathbb{L} [f(x)]=\int _0 ^{\infty} e^{-sx}f(x)dx. The Attempt at a Solution...

You see this picture of the second fundamental theorem of calculus and you are taught in high school / early college calculus that the t is a dummy variable. However, couldn't you view this as some sort of transform? You convert a function f(t) into a function of f(x). Is this a valid way to...

##\mathcal{L}\{f(t)\}=F(s)## \mathcal{L}\{e^{at}\}=\frac{1}{s-a},Re(s)>a \mathcal{L}\{\sin (at)\}=\frac{a}{s^2+a^2}, \quad Re(s)>0 \mathcal{L}\{\cos (at)\}=\frac{s}{s^2+a^2},Re(s)>0 If we look at Euler identity ##e^{ix}=\cos x+i\sin x##, how to get difference converge intervals...

Why would we want to transform a vector in our normal basis (xyz axes) to another basis? The only situation I can recall is when we are looking at a force applied on an inclined plane. Are there any other real life examples where this may be necessary?

L[sin(at)]=\frac{a}{s^{2}+a^{2}}, Re[s]>0 L[e^{kt}]=\frac{1}{s-k}, s>k L[e^{-kt}]=\frac{1}{s+k}, s<-k L[sin(at)]=\frac{1}{2i}L[e^{iat}-e^{-iat}] =\frac{1}{2i}L[e^{iat}]-L[e^{-iat}] Using the above relations =\frac{1}{2i}[\frac{1}{s-ia}-\frac{1}{s+ia}], s>ia, s<-ia The problem is...

Hi all, This question is on the Hilbert transform, particularly on the domain of the input and output functions of the Hilbert transform. Before rising the question, consider the Fourier transform. The input is f(t) and the output is F(\omega). The function f and F are defined over...

Hi, I am having some difficulty doing the integral ∫d^{3}v1d^{3}v2 | \overline{v1}-\overline{v2}|, where u1\leq|v1|,|v2|\lequ2, and \overline{v1} means vectors. It seems better to evaluate it in the center of mass frame, by substitution \overline{v1}+\overline{v2}=\overline{V}, and...

Is there a name for a transformation using the orthonormal base s_k(x)=\lceil \sin kx \rceil,\: c_k(x) = \lceil \cos kx \rceil \quad ? So basically a Fourier transform or Fourier series using periodic rectangles. What are the properties? Is there some kind of convolution theorem?

I am having trouble with this homework problem, I know how to get started but I just don't know how to carry through the completion of the problem: Question: Given the Fourier transform of an aperiodic signal X(ω) = 2*sin(3(ω-2π))/ω-2π (a)find its inverse Fourier transform x(t) using...

\mathcal{L}\{f(t)*g(t)\}=F(s)G(s) Is there some relation between F(s)*G(s) and f(t)g(t)? ##*## is convolution.

Homework Statement Transform the line element of special relativity from the usual (t, x, y, z) coordinates rectangular coordinates to new coordinates (t', x', y', z') related by t =\left (\frac{c}{g} + \frac{x'}{c} \right )sinh\left (\frac{gt'}{c} \right) x =\left (\frac{c}{g} +...

In relativistic limit the spin and the angular momentum are not of conservation because of spin-orbit interaction.Then the symmetry SU(2) is broken because vector spin does not commute with the interaction Hamintonian.The SO(3) symmetry is also broken for the same reason.So I do not understand...

Homework Statement Laplace Transform teat Homework Equations The Attempt at a Solution http://img521.imageshack.us/img521/6449/homeworkhelp.jpg Not sure where I am going wrong. I feel like I did integration by parts incorrectly, because the anser I have boxed is not the...

Homework Statement Let's say that I have a set called M, which is a subset of real numbers. Let's say that I want to create a sequence {s_1, s_2, ..., s_3} with all of the members of M, which would be ordered in an ascending (increasing) order. For example, if M = {4, 5, 1, 3, 2}, then s_0 = 1...

"Sketch the form of the Fourier transform" - is this right? Question ~ sketch the "form of the Fourier transform" for the function: f(k) = sin^2(ka/2) / (ka/2)^2So I'm thinking it will look like a cos [or sin] graph (shifted so that its 'above' *f(k)=0*) and that there will be some sort...

I am trying to find a real life inverse linear transform which can be used to motivate students. Does anyone have an example or two? I am looking for an example which will have a real impact. Thanks in advance.

I am trying to find a real life inverse linear transform which can be used to motivate students. Does anyone have an example or two? I am looking for an example which will have a real impact. Thanks in advance.

Homework Statement f(t) is a piecewise function: {0 0<= t< 1 {t*exp(2t) t = >1Homework Equations F(s)= L{f(t)}The Attempt at a Solution F(s)= L{t*exp(2t)} for this problem I just took the Laplace Transformer directly from the table which is: n!/ (s-a)^(n+1) and after plucking in the...

Homework Statement S(t) = S(0)e^{-i \pi f_{o}t} e^{-t/T^{*}_{2}}, 0 \leq t < \infty S(t) = 0, t < 0 Show that the spectrum G(f) corresponding to this signal is given by: G(f) = S(0) { \frac{T^{*}_{2}}{ 1 + [2 \pi (f- f_{o} )T^{*}_{2}]^{2}} + \frac{i2 \pi (f- f_{o} )...

Hello, I am confused as to how to transform nonlinear ODEs to linear ones by change of variables. Usually its pretty straight forward and I can do it, but this particular problem has me stumped and I don't know where to begin. Homework Equations Thank you guys!

I want to perform the inverse of \frac s { [(s+α)^2-β^2](s^2+ω^2)} I know the conventional way is \frac s { [(s+α)^2-β^2](s^2+ω^2)}= \frac{As+B}{[(s+α)^2-β^2]}+\frac{Ds+E}{(s^2+ω^2)} s= (As+B)(s^2+ω^2)+(Ds+E)[(s+α)^2-β^2] \Rightarrow\; A+D=0,\; B+E+2\alpha...

Homework Statement Find f(t) for: 2\int_{0}^{t}f'(u)sin(9(t-u)du +5cos(9t), t\geq0 The Attempt at a Solution F(s)=2\frac{9(sF(s)-f(0))}{s^2+81}+\frac{5s}{s^2+81} At this point i don't know what to do with f(0) since there are no initial conditions. What do I do with it?

Homework Statement I've been stuck on this for a while: Find the Fourier transform of f(t)=sin(\omega0t+\phi) Homework Equations I know that I have to use F(ω)=\intf(x)e^-iωt dt (between - and + infinity) to solve this The Attempt at a Solution So far I have...

I really need your help - i can't work out how to do a FFT in excel. The main problem is I don't have a constant sampling rate - I recorded the time and then the corresponding magnitude of the wave. I have followed everything oneline but I can't seem to get anything to work as I can't fill the...

now say we have cos^2(3t), how would you go about computing it with the 3t? i can manage cos^2(t) but I'm not sure how to take it that one step further in the link below is what I've managed so far.. [SIZE="5"]SOLVEDI worked it out. If anyone's interested in the future, Just start it off as...

Homework Statement Any wavepacket can be obtained by the superposition of an infinite number of plane waves using the so-called Fourier integral or Fourier transform f(x,t) = \frac{1}{\sqrt{2\pi}} _{-\infty}\int^\infty A(k)e^{i(kx-\omega t)} dk Find at t=0 the representation of the...

I am trying to do laplace transform of y(t)=e^{-at}\cos (bt)\;. The answer should be: \frac {s+a}{(s+a)^2+b^2} But here is my work, I can't get rid of the -ve sign. I must be too blind to see the obvious, please help: \overline{y(s)}=\int^∞_0 e^{-(s+a)t}\cos (bt) dt\;=\; \frac 1 b...

Homework Statement d'^2 (y)/dt + 4 (dy/dt) + 4y = -7(e^(-3t)). Here I need to forced response of this differential equation using laplace transform technique. Homework Equations The Attempt at a Solution I understand the part of converting each term to each laplace, d^2y/dt to...

Show G(k)=\sqrt{2π}g1(k)g2(k) Given that G(k) is the Fourier transform of F(x), g1(k) is Fourier trans of f1(x), g2(k) is Fourier trans of f2(X) and F(x)=^{+∞}_{-∞}∫dyf1(y)f2(x-y) SO FAR G(k)=1/\sqrt{2π}^{+∞}_{-∞}∫F(x)e-ikxdx <-def'n of Fourier transform...

Hi, I am taking a random process class and I came across a problem that has stumped me. I believe I know the end result but I would like to know how it is solved. I have been out of college for a while and I am a little rusty with integration. Homework Statement What I need is to find out...

Hi, my name is Tim, I am new to this forum. Here's the description: I don't understand how they've done it. I realize I can plot this, but what is the logic. As a graph, I drew ln(-x) first, then added 3, so move left by 3 but that was not correct I can see they've added 3 first, move...

Homework Statement Let u1 = [1 1]^T and u2 = [0 -1]^T. Find a 2 x 2 real matrix A so that the function T_A is a map from ℝ^2 to ℝ^2, given by multiplication by A, T_A := Av, sends T_A(u1) = v1 and T_A(u2) = v2 where v1 = [cosθ sinθ]^T and v2 = [-sinθ cosθ]^T. Explain/justify your...

Show the diffusion equation is invariant to a linear transformation in the temperature field $$ \overline{T} = \alpha T + \beta $$ Since $\overline{T} = \alpha T + \beta$, the partial derivatives are \begin{alignat*}{3} \overline{T}_t & = & \alpha T_t\\ \overline{T}_{xx} & = & \alpha T_{xx}...

how to get the Fourier transform of (1+at^2)^-n ? n is a natural number such that (n>1) and a is any positive number. i.e. ∫((1+at^2)^-n)*exp(-jωt)dt; limits of integration goes from -∞ to ∞

Dear All, I have encountered the following situation: Given a node that is connected through n resistors to n ports. One if the resistors is a negative resistance and equals to minus of all other resistors in parallel. \frac{1}{R_n} =- \sum_{i=1}^{n-1} \frac{1}{R_i} Using the well known...

Homework Statement Find the Fourier transform of x(t) = e-t sin(t), t >=0. We're barely 3 weeks into my signals course, and my professor has already introduced the Fourier transform. I barely understand what it means, but I just want to get through this problem set.Homework Equations I...

maple issue -- inverse laplace transform equation from a basic series RLC circuit Pretty simple for some of you I know, but I have a laplace transform equation from a basic series RLC circuit ((sV-v(0))/L+si(0))/(s^2+sR/L+1/LC) = I(s) I want to take the inverse laplace of it, I am given all...

I'm inverting this: Y = s2 + 15s + 17 / [(s+1)(s2 + 13s - 4)] I'm using PF expansion, A/(s+1) + Bs + C/(s2 + 13s - 4), I however keep on getting wrong answers, seeing how Runge-Kutta and Taylor approximation disagrees with my final equation. My final equation is...

Hi all, I have a seemingly simple problem which is I'd like to efficiently evaluate the following sums: Y_k = \sum_{j=0}^{n-1} c_j e^{\frac{i j k \alpha}{n}} for k=0...n-1. Now if \alpha = 2\pi, then this reduces to a standard DFT and I can use a standard FFT library to compute the...

Homework Statement Hi I am trying to solve the following system of ODE's by Laplace transforming: x' = 1 + 21y - 6x \\ y' = 6x-53y with the initial conditions x(0)=y(0)=0. Laplace transforming gives me (X and Y denote the Laplace transformed variables) sX = 1 + 21y-6x \\ sY = 6x-53y From...

This is for an assignment, (not sure if its in the right section) but anyway I'm considering the system response to H(w) = 10/(jw + 10) when the input is x(t) = 2 + 2*cos(50*t + pi/2) so I know that Y(w) = X(w).H(w) but I'm not sure what to do about the '2 + ' in the input. I know that...

H is a contravariant transformation matrix, M is a covariant transformation matrix, G is the metric tensor and G-1 is its inverse. Consider an oblique coordinates system with angle between the axes = α I have G = 1/sin2α{(1 -cosα),(-cosα 1)} <- 2 x 2 matrix I compute H = G*M where M =...

Homework Statement The argument of the kernel of the Fourier transform has a different sign for the forward and inverse transform. For a general function, show how the original function isn’t recovered upon inverse transformation if the sign of the argument is the same for both the forward and...

Hi, I was wondering if anyone might know what the analytic Fourier transform of a Super-Gaussian is? cheers

Since I lack the understand of real world applications of Fourier Transform in the real world I decided to buy a signals and systems book (Lathi) do some Fourier Transform problems and them do the same problem in Matlab. The question in the book wants me to find the Fourier Transform of...