Transform Definition and 1000 Threads

Homework Statement Let F be the 4x4 matrix whose (i, j)th entry is 5ij in F_13 for i, j = 0,1,2, 3. Compute F(hat) and verify that F(hat)F = I Homework Equations The matrix F(hat) is called the inverse discrete Fourier transform of F. The Attempt at a Solution I found that e = 4...

Homework Statement (i) Verify that 5 is a primitive 4th root of unity in F13. (ii) Let F be the 4x4 matrix whose (i, j)th entry is 5ij in F13 for i, j = 0,1,2, 3. Compute F(hat) and verify that F(hat)F= I. Homework Equations The matrix F(hat) is called the inverse discrete Fourier...

Homework Statement [SIZE="4"]Evaluate the Laplace of {tcos4t} using the derivative of a transform Ofcourse i know the shortcut way of doing this, but I need to do it the long way. Homework Equations shortcut way t cos bt =[SIZE="5"] \frac{s^2-b^2}{(s^2+b^2)^2} long way...

We have a few posters struggling with this, I thought I'd post a step by step guide, to see if it would help. That seems easier than trying to untangle the confused threads we have. We'll see if it works... Setup and notation: We have a rocket, which has a front and a back. We have a...

Hey! :o Could you give me a hint how to prove the following property of the Fourier transform, when $F[f(x)]=\widetilde{f}(x)$, where $F[f(x)]$ is the Fourier transform of $f(x)$? $$F[ \widetilde{f}(x) ]= \frac{f(-k)}{2 \pi}$$ We know that: $ \widetilde{f}(k)=\int_{- \infty}^{+ \infty}{...

Homework Statement Use the Fourier transform directly to solve the heat equation with a convection term u_t =ku_{xx} +\mu u_x,\quad −infty<x<\infty,\: u(x,0)=\phi(x), assuming that u is bounded and k > 0. Homework Equations fourier transform inverse Fourier transform convolution thm The...

Homework Statement using a rotation transform, show that the plane z = b - y can be transformed to the horizontal plane \widehat{z} = \frac {b} {\sqrt{b^2 + c^2}} Homework Equations ^ The Attempt at a Solution I just need some help understanding the question, if I could get a...

Homework Statement Take the inverse Fourier Transform of 5[\delta(f+100)+\delta(f-100)]\bigg(\frac{180+j2\pi f*0.0135}{1680+j2\pi f*0.0135}\bigg)Homework Equations g(t)=\int_{-\infty}^{\infty} G(f)e^{j2\pi ft}dt The Attempt at a Solution g(t)=\int_{-\infty}^{\infty}...

Homework Statement Without solving the differential equation, find the differential equation that solves Fourier transformation of given differential equation for ##a>0##. a) ##y^{'}+axy=0## b) For what ##a## is the solution of part a) an eigenfunction of Fourier Transform Homework Equations...

Homework Statement Calculate (from the definition, no tables allowed) the Fourier Transform of e^{-a*|t|}, where a > 0. Homework Equations Fourier Transform: G(f) = \int_{-\infty}^{\infty} g(t)e^{-j\omega t} dt The Attempt at a Solution I thought I'd break up the problem into the two cases...

Homework Statement Suppose f(x), -\infty<x<\infty, is continuous and piecewise smooth on every finite interval, and both \int_{-\infty}^\infty |f(x)|dx and \int_{-\infty}^\infty |f'(x)|dx are absolutely convergent. Show the Fourier transform of f'(x) is i\mu F(\mu).Homework Equations...

A necessary condition that a function f(x) can be Fourier transformed is that f(x) is absolutely integrable. However, some function, such as |t|, still can be Fourier transformed and the result is 1/w^2, apart from some coefficients. This can be worked out, as we can add a exponential...

Homework Statement "Suppose x[n] is a DT (discrete time) periodic signal with fundamental period N. Let us define x_{n}[n] to be x[n] for n ε {0, 1,2, ... , N-1} and zero elsewhere. Denote the Fourier transform of x_{n}[n] with X_{n}[e^jω]. How can one find the Fourier Series coefficients...

hello pf! i am wondering if anyone here knows of a geometric, intuitive explanation for the laplace transform? if so, please direct me to the source of if you could, explain to me your understanding? thanks!

1. Given: The DTFT over the interval |ω|≤\pi, X\left ( e^{jω}\right )= cos\left ( \frac{ω}{2}\right ) Find: x(n) 2. Necessary Equations: IDTFT synthesis equation: x(n)=\frac{1}{2\pi}\int\limits_{-\pi}^{\pi}X\left ( e^{jω} \right ) e^{j\omega n}d\omega Euler's Identity...

Homework Statement Determine the Fourier Transform of the function shown. Plot the result using excel, MathCad, or Matlab. See attachment for figure of triangle above x-axis from -X0/2 tp X0/2 with a max height of 1 at x=0. Homework Equations The answer is F(k) = X0/2 [sin(kX0/4) /...

Hi, I have problems finding out the Fourier transform of the following function, 1/\sqrt{q^2 + m^2}, where m\neq 0 denotes a parameter. It seems easy, but I don't know how. Could anybody show me how to do it ? Thanks in advance. hiyok

Homework Statement Find the inverse Fourier transform of f(w)=1 Hint: Denote by f(x) the inverse Fourier transform of 1 and consider convolution of f with an arbitrary function. Homework Equations From my textbook the inverse Fourier transform of f(w)=\int F(w)e^-iwt dw The...

How to transform a random variable CDF to a standard normal Given F(x) = 1- exp (-sqrt x), for x greater that 0 Thanks.

Dear Physics Buddies, How are well all, okay I hope. I was wondering if I might browse all your infinite intellects and ask you a very simple question. I am working with some medical images in MATLAB and my collaborators would like to know the orientation of the fibres that it contains...

After searching on the web and reading a bit, I found that lenses can perform Fourier transform. All you need to do is put a transparant object in front of it, like a transparant sheet with black stripes on it and a screen behind the lens(so basically a 4f setup). The lens will then perform a...

So the complex exponential Fourier series form an orthonormal basis for the space of functions. A periodic function can be represented with countably many elements from the basis, and an aperiodic function requires uncountably many elements. Given a signal, we can find the coefficients of the...

\[ \frac{(s+1)^2}{s^2 - s + 1} \] I have simplified it down to \[ \frac{s - \frac{1}{2} + s^2 + s + \frac{3}{2}}{(s - 1/2)^2 + \frac{3}{4}} = e^{1/2t}\cos\Big(t\frac{\sqrt{3}}{2}\Big) + \sqrt{3}e^{1/2t}\sin\Big(t\frac{\sqrt{3}}{2}\Big) + \frac{s^2 + s}{(s - 1/2)^2 + \frac{3}{4}} \] but I can't...

Using geometric evaluation of the magnitude of the Fourier transform from the corresponding pole-zero plot, determine, for each of the following Laplace transforms, whether the magnitude of the corresponding Fourier transform is approximately lowpass, highpass, or bandpass. \[ H_1(s) =...

With a Laplace transform, we can remember common set ups; for example, \[ \mathcal{L}\{e^{-at}\} = \frac{1}{s + a}. \] When it comes to the inverse Laplace transform, I can only find the tables to remember in a book. However, if we go back to the Laplace transform, we can always do \[...

Homework Statement the function is Exp[-w^2]/w^2, how to solve the Fourier transform analytically with Residue theorem? It is better if there is more general results. Mathematica can solve it analytically, but I need a human-soluable way. Homework Equations The Attempt at a...

##\varphi(p)=\frac{1}{\sqrt{2\pi\hbar}}\int^{\infty}_{-\infty}dx\psi(x)e^{-\frac{ipx}{\hbar}}##. This ##\hbar## looks strange here for me. Does it holds identity ##\int^{\infty}_{-\infty}|\varphi(p)|^2dp=\int^{\infty}_{-\infty}|\psi(x)|^2dx=1##? I'm don't think so because this ##\hbar##. So...

Hi, I have seen textbooks model how an electric field of an electron changes when viewed from another frame of reference. In these models, the electric fields seems to "compress" along the axis of motion. What happens to the magnetic moment in these situations? Does the magnetic moment also get...

Question on my study guide: An optical systems consists of 4 lenses spaced apart. Each lens has a focal length f. Each lens is located a distance "z" away from each plane as shown. The total length of the system is 8z. Find the distance z needed to satisfy a FOURIER TRANSFORM condition...

Hello, I was wondering if one can give meaning to the Fourier transform of the linear function: \int_{-\infty}^{+\infty} x e^{ikx}\, dx I found that it is \frac{\delta(k)}{ik} , does this make sense?

Okay, I am trying to determine the Fourier transform of cos (2\pix)=f(x) Where F(k)=^{\infty}_{\infty}\intf(x)exp^{-ikx} dx, So I use eulers relation to express the exponential term in terms of cos and sin, and then I want to use sin/cos multiplication integral results, such as...

Homework Statement Homework Equations sinc(x) = \frac{sin(x)}{x} The Attempt at a Solution bit unsure how to get started?? i know transform of rectangular pulse pτ(t)=τ*sinc(τω/2∏) also that sin(ωt)= ejωt-e-jωt / (2) I could also probably sketch sinc(t/2∏), if that helps.

Dear all, I have recently come across the following Fourier transform (FT): I=\int_{-\infty}^{\infty} dx \, e^{-\imath x t} \frac{(1-x^2)}{(1+x^2)^{3/2} (a^2+x^2)}. The integrand contains two branch points on the imaginary axis, plus two poles also residing on the imaginary...

The typical way to evaluate $ \displaystyle \int_{0}^{\infty} \frac{\cos mx}{a^{2}+x^{2}} \ dx$ is by contour integration. In a recent thread I evaluated that integral using the Laplace transform. http://mathhelpboards.com/analysis-50/advanced-integration-problem-9129.html#post42551My...

Hello, As of recently, I've been working with Laplace transforms and have a question about their relationship to solving differential equations. I know the definition of the laplace transform and I know that a function is essentially being transformed from the time domain to complex...

I understand that the Fourier transform maps one function onto another. So it is a mapping from one function space onto another. My question is, why is it often referred to as a mapping from time domain to the frequency domain? I don't understand why the image of the Fourier transform...

Hi Guys, I have an expression that i am struggling to manipulate into a laplace transform. This expression should fit one or a combination of the common transform pairs. I believe the transform the expression should be fitting is either a unit step 1/s a unit ramp 1/s^2 an exponential 1/s+a...

Hi, I would like to find the inverse Laplace transform for 11/(s^2+16)^2 I have tried to expand it using the following partial fraction decomp to find the constants and take the inverse Laplace but this did not work C1(s)+ C2/(s^2+16) + C3(s)+C4/(s^2+16)^2 Does anyone have any suggestions?

Homework Statement Hi I would like to know how to expand 20/2s(s^2+9) in order to find the inverse Laplace Transform of the function K(s) to gt k(t). The (s^2+9) term in the denominator is throwing my calculations off for the constants because of the s^2 term. Homework Equations...

Hello, I have a relatively simple question. after being unable to find it through google I have decided to ask you guys if you know what the Laplace transform of a unit step function that looks like this would look like Us(t-2) From tables, the Laplace transform for a regular units step...

Hi guys, I've been using this site for a while now, but this is going to be my first post. I want to pick your brains to get some insight on this problem I'm tackling. I'm trying to take a Fourier Transform of a function. My function is a function of (r,phi) and it is a piecewise function...

Homework Statement Using the Schwarzschild Metric and the Contravariant Position Vector 1x4 ##x^k## with 4 vector: $$x^{k'} = \left[ \begin {array}{c}r \\ \theta \\ \phi \\ t \end {array} \right]$$ where ##x^1## = r = 1 per unit distance ##x^2## = ##\theta## = 50 Degrees ##x^3##...

Homework Statement Is there a way to evaluate L^{-1}(\frac{F(s)}{s + a})? I'm sure if it can be evaluate. Homework Equations The Attempt at a Solution

Given the transfer function \[ H(s) = \frac{Y(s)}{U(s)} = \frac{1}{s + 1} \] and \[ u(t) = 1(t) + 1(t - 1). \] How do I find U(s)? I know I take the Laplace transform of u(t) but with the two step functions how can this be done? The Laplace transform of the step function is \(\frac{1}{s}\)...

I can't seem to part of an inverse Laplace transform correct. \begin{align*} f(t) &= \frac{6}{5}\mathcal{L}^{-1}\bigg\{\frac{1}{s + 2}\bigg\} + \frac{3}{5}\mathcal{L}^{-1}\bigg\{\frac{3s - 1}...

Homework Statement Find the Laplace transform of f(t) = t \forall 0≤t≤T, 0 otherwise Homework Equations The Attempt at a Solution I write the function as tu(t)-t*u(t-T) That is turn on the function t at t=0 and turn the function t off at t=T. It seems to be right to me...

Hi~ I recently solve a Laplace transform problem as following L[int{t,0}cosh(t'-1)U(t'-1)dt']=? U(t'-1) is the unit step function(=1 for t'>1, =zero otherwise) According the standard Laplace formula : (1)L[cosh(t-1)U(t-1)]=exp(-s)*s/(s^2-1); (2)L(int{t,0}f(t')dt')=F(s)/s...

Hello, I was wondering if such a thing even exists, so here it goes... Let's say I have a function x(s) (it is real, smooth, differentiable, etc.) defined on (0,1). In addition, dx/ds = 0 on the boundary (s=0 and s=1). I can compute its Fourier transform (?) as a_p = \int_0^1 x(s)...

Hi, I hope somebody can help me with this one. Homework Statement Compute the Fourier Transform of the distribution x-a Homework Equations The Fourier Transform of a distribution is just the distribution evaluated with the Fourier Transform of a test function.The Attempt at a Solution See...

I have an exercise with a function of the form: h(t) = f(t)g(t) and f(t) and g(t) both have discrete Fourier series, which implies that h does too. I want to find the Fourier series of h, so my teacher said I should apply the convolution theorem which would turn the product above into a...