Transform Definition and 1000 Threads

Homework Statement Determine the inverse Laplace transform Homework Equations 3s+9/(s+3)^2+7 The Attempt at a Solution Converted to 3s+9/s^2+6s+16 to try and use the partial fractions method but getting nowhere. I'm Not sure if Iam making the question more difficult, can't seem to put the...

Hello, for a function f∈L2(ℝ), are there known necessary and sufficient conditions for its Fourier transform to be zero only on a set of Lebesgue measure zero?

Homework Statement I want to invert a function from Laplace transform space to normal space. Homework Equations In Laplace transform space, the function takes the form $$ \bar f (s) = \frac{\exp\left[ x (-a +\sqrt{a^2+ b +c s} )\right]}{-a +\sqrt{a^2+ b +c s}}. $$ Here, ##s## is the Laplace...

Hi Guys, I have an equation I'm trying to work out if it 'Laplaceable'? As in, can I get a transfer function? d2y(t)/dt2 = k⋅cos(Φ)⋅y(t)

[##f^*## represents complex conjugate of ##f##. ] [##\widetilde{f}(k)## represents Fourier transform of the function ##f(x)##.] $$\begin{align} \int_{-\infty}^{\infty}f^*(x)e^{ikx}\,dx&=\int_{-\infty}^{\infty}f^*(x)\left(e^{-ikx}\right)^*\,dx\\...

Given the Fourier conjugates ##\vec{r}## and ##\vec{k}## where ##\vec{r} = [r_1,r_2,r_3]## and ##\vec{k} = [k_1,k_2,k_3]## , are ##r_1## /##k_1##, ##r_2##/##k_2##, ##r_3##/##k_3## also Fourier conjugates, such that: ##\begin{equation} \begin{split} f(\vec{r})&=[f_1(r_1),f_2(r_2),f_3(r_3)] \\...

Homework Statement Homework Equations N/A The Attempt at a Solution The left hand side (red box) is the data sheet provided to us in the exam. The right hand side (blue box) is Wolfram Alpha. The data sheet says that the inverse Laplace transform of 1/s is equal to u(t) (i.e. the unit step)...

Homework Statement Show that ## \int\limits^{\infty}_0 \sum\limits^{\infty}_{n=1}e^{-\pi n^{2} t} t^{s-1} dt = \sum\limits^{\infty}_{n=1}(\pi n^{2} )^{-s} \int\limits^{\infty}_{0} e^{-t} t^{s-1} dt ## Homework Equations ##\Phi (t)=\theta(it/2)=1+2\sum\limits^{\infty}_{n=1}e^{-\pi n^2 t}. ##...

I have some understanding of Liner Energy Transfrom (LET), but when I compare it with other terminologies such as momentum, then it gets little contradicting. For example, I know that if talk about particles and ions, then a gold ion (AU) has much higher LET than an Iron particle (Fe). And...

Homework Statement Solve ut+3ux=0, where -infinity < x < infinity, t>0, and u(x,0)=f(x).Homework Equations Fourier Transform where (U=fourier transform of u) Convolution Theorem The Attempt at a Solution I've used Fourier transform to get that Ut-3iwU=0 and that U=F(w)e3iwt. However, I'm...

Homework Statement Link: http://i.imgur.com/JSm3Tqt.png Homework Equations ##\omega=2\pi t## Fourier: ## Y(f)=\int ^{\infty}_{-\infty}y(t)\mathrm{exp}(-j\omega t)dt## Linearity Property: ##ay_1(t)+by_2(t)=aY_1(f)+bY_2(f)##, where a and b are constants Scaling Property...

Homework Statement Homework EquationsThe Attempt at a Solution 1 ##3u(t)-3u(t-2)## ##\frac{3}{s}-\frac{e^{-2s}3}{s}## 2 ##\frac{5t}{2}u(t)-\frac{5t}{2}u(t-2)## ##\frac{5}{2s^2}-\frac{5e^{-2s}}{2s^2}## 3 I have no idea how to do this one.

We have a waveform that is composed of several waves, maybe something like this: If we Fourier transform the graph we get something like this: My question is, does the value of the largest column represent the peak to peak voltage of the waveform pictured above?

Homework Statement Can someone check my work? Homework EquationsThe Attempt at a Solution 1. ##\frac{1}{s+2}+\frac{1}{s^2+1}## 2. ##\frac{2}{s}+\frac{3}{s+4}## 3. ##\frac{s*sin(-2)+cos(-2)}{s^2+1}## 4. ##\frac{1}{(s+1)^2}## 5. Don't really know how to do this one...

Hi, everyone, the question is as below: Find the inverse Laplace transform to 1/(350+s) * X(s). 's' is the Laplace variable and 'X(s)' is also a variable. I inverted 1/(350+s) and X(s) separately and multiplied them together directly. But this seems not giving me the correct answer. Could...

Hi Guys, I'm having trouble with the following: A finite-time signal is the result of a filter G(t) applied to a signal. The filter is simply “on” (1) for t ∈ [0,T] and off (“0”) otherwise. If x(t) is the signal, and x(ω),its Fourier transform, compute the Fourier transform of the filtered signal...

Can anyone explain what does the author mean by the statement below? page 27 of this paperI don't understand the relation between the Fourier transform and translational invariance. Thanks

Not homework question, just need clarification and explanation. How did the person get from the left equation to the right side. I know he's just simplifying. But he didn't include steps and I've been trying to work out how to no avail. Any help on how this person simplified the LHS to RHS? Thanks!

The Lorentz transformation operator acting on an undotted, i.e. right-handed, spinor can be expressed as $$e^{-\frac{1}{2} \sigma \cdot \mathbf{\phi} + i\frac{1}{2} \sigma \cdot \mathbf{\theta}}.$$ There is a very cool, almost childlike, derivation of this expression in Landau Vol. 4 S. 18 I've...

In case the orientation of a primitive cell is not what I want, is there tools to do a user-supplied 3D rotation to bring the primitive cell to the preferential orientation and output the new coordinates? Thanks,

Problem F denotes a forward Fourier transform, the variables I'm transforming between are x and k - See attachment Relevant equations So first of all I note I am given a result for a forward Fourier transform and need to use it for the inverse one. The result I am given to use, written out...

Does a static uniform E field in space appear to be a mix of E and B fields to an observer on Earth (ignoring the Earth's motion)? My GR is not so great, but would the rigorous way to calculate the new fields be to parallel transport the Maxwell 2-form ##F_{\mu\nu}## from free space, where it...

Hello all, First time poster here so please excuse any mistakes as I'm unfamiliar with the conventions of this forum. Also before I get started I'd like to say I wasn't sure exactly where a question like this would go; I debated in the Math Programs and Latex section but figured general physics...

I've tried to read the reason for using Fourier transform in wave packets, I don't understand why. Please help me with this.

OK, my understanding is that the characteristic equation for a matrix is similarity-invariant, from which results that the trace & determinant - which correspond to the penultimate & free coefficients of the characteristic equation - and other parameters (corresponding to other coefficients) are...

Homework Statement Solve: y''+λ^2y = cos(λt), y(0) = 1, y'(π/λ) = 1 where t > 0 Homework EquationsThe Attempt at a Solution I start off by taking the Laplace transform of both sides. I get: L(y) = \frac{s}{(s^2+λ^2)^2}+\frac{sy(0)}{s^2+λ^2}+\frac{y'(0)} {s^2+λ^2} Now take the inverse...

Homework Statement find the inverse Laplace transform of the given function by using the convolution theorem Homework Equations F(s) = s/((s+1)(s2)+4) The theorem : Lap{(f*g)(t)} = F(s)*G(s) The Attempt at a Solution I know how to find it the answer is : we have 1/(s+1) * s/(s+4) and the...

Hi! I'd like to smear an audio recording, where the frequency content audibly changes, into an audio recording where it does not. Here's a recording of a sampled piano playing a melody, which will serve as an example: https://dl.dropboxusercontent.com/u/9355745/oldmcdonald.wav The frequency...

Homework Statement We want to find the Laplace transform for f(t): 0 for t≤2 and (t-2)2 for t≥2 Homework Equations I know that Lap{uc f(t-c)} = e-csLap{f(t)}=e-csF(s) I rewrite f(t)=0+g(t) where g(t) = 0 for 0≤t<2 and (t-2)2 for t≥2 so we can write f(t)=g(t)= u2(t)*(t-2)2...

Hello I am trying to determine the Fourier transform of the hyperbolic tangent function. I don't have a lot of experience with Fourier transforms and after searching for a bit I've come up empty handed on this specific issue. So what I want to calculate is: ##\int\limits_{-\infty}^\infty...

Homework Statement Homework Equations transformation The Attempt at a Solution u = x-y v = x+y I convert each side in terms of u, v, get: u = 0, u = -2 v = 2, v = 4 Correct?

Homework Statement Find Req in the given circuit Homework Equations Series: req = r1+r2... parallel: 1/req = 1/r1 + 1/r2 ... The Attempt at a Solution Without redrawing the circuit I do: 12||60 = 10 10+20 = 30 30 || 30 = 15 15+10 = 25 25||25 = 12.5 12.5+15+5 = 32.5 = Req This is the correct...

Homework Statement The (computing) task at hand is to take a function f(x) defined at 2N discrete points, and use the Discrete Fourier Transform (DFT) to produce F(u), a plot of the amplitudes of the frequencies required to produce f(x). I have an array for each function holding the value of...

Homework Statement [/B] This is a computing coursework problem. (There is a reasonably long theory preamble). Create a single slit centred on the origin (the centre of your array) width 10 and height 1. The array containing the imaginary parts will be zero and the array containing the real...

Homework Statement I have to do nodal analysis and I was wondering if there is any transformations or simplifications I can do to the circuit. In this class we are supposed to be able to look at the circuit and input what we need into the matrix based on just looking at it. I am not sure that I...

Homework Statement Given x(t)=8cos(70\pi t)+4sin(132\pi t)+8cos(24\pi t), find the Fourier transform X(f) in the form of \delta function. Homework Equations X(f)=\int ^{\infty}_{-\infty}x(t)e^{-j\omega _0t}dt cos(\omega t)=\frac{e^{j\omega t}+e^{-j\omega t}}{2} sin(\omega t)=\frac{e^{j\omega...

Hello - I'm not sure this is where this should go, but I'm working with Laplace Transforms and differential equations, so this seems as good a place as any. Also, I doubt this is graduate level math strictly speaking, but I went about as high as you can go in calculus and linear algebra during...

Homework Statement Evaluate the Fourier Transform of the damped sinusoidal wave g(t)=e^{-t}sin(2\pi f_ct)u(t) where u(t) is the unit step function. Homework Equations \omega =2\pi f G(f)=\int ^{\infty}_{-\infty} g(t)e^{-j2\pi ft}dt sin(\omega _ct)=\frac{e^{j\omega _ct}-e^{-j\omega _ct}}{2j}...

I am using ROOT to calculate the Fourier transform of a digital signal. I can extract the individual parts of the transform, the magnitude and phase in the form of a 1D histogram. I am attempting to reconstruct the transforms from the phase and magnitude but cannot seem to figure it out. Any...

Homework Statement The following series are not power series, but you can transform each one into a power series by a change of variable and so find out where it converges. ∑∞0 ((3n(n+1)) / (x+1)n Homework Equations a power series is a series of the form: a0 + a1x + a2x^2 ... + ... The...

My first thought was simply that the Fourier transform of a sum of Gaussians functions that are displaced from the origin by different amounts would just be another sum of Gaussians: F{G1(x) + G2(x)} = F{G1(x)} + F{G1(x)} where a generalized shifted Gaussian is: G(x) = G0exp[-(x - x0)2 / 2σ2]...

Hello everyone, I was trying to develop a sort of generalized version of the Fourier Transform. My question in particular is: Given a function f(x,u), is there a function g(x,u) with \int_{-\infty}^\infty f(x,u)g(x,u')\mathrm{d}x=\delta(u-u') For f(x,u)=e^{2\pi ixu} the solution would be...

A minha pergunta é na divisão 10800/1110 My question is in the division 10800/1110 ?

Homework Statement This isn't exactly a "problem" per se , but I need to understand it for a course I'm taking. I'm trying to understand the significance and when to use the vector conversion matrices, or just the identities. I'll use an example that I made up, using rectangular to polar...

Homework Statement ##A\dot{x} + By = 0## ##C\dot{y} + Dx = 0##Homework Equations ##\int u'v = uv - \int uv'## The Attempt at a Solution This is a system of linear DE: ##A\dot{x} + By = 0## ##C\dot{y} + Dx = 0## Where the constants A-D are non-zero and x and y are functions of time. This is...

A tad embarrassed to ask, but I've been going in circles for a while! Maybe i'll rubber duck myself out of it. If $$f(t) = f(t+T)$$ then we can find the Fourier transform of $$f(t)$$ through a sequence of delta functions located at the harmonics of the fundamental frequency modulated by the...

I am using a Tascam recorder to record an environmental nuisance noise that is occurring in my home. I then use Virtins Multi Instrument Software, which includes an oscilloscope, band pass filter, and a spectrum analyser. Noise source is probably machinery at a legal marijuana grow op. That...

As the Heaviside function is a function of t - 4, that means all other terms must also be functions of t - 4. The sine function is, but the exponential isn't. However with a little manipulation, we get $\displaystyle \begin{align*} f\left( t\right) &= \mathrm{H}\,\left( t - 4 \right) \,\sin{...

I am a little familiar with Fourier Analysis, but I don't know where to get tools to get the answer to this question: Consider a discrete signal A[0..N-1], consisting of N samples. Suppose we Fourier transform it and get a series of harmonics. Now, consider the discrete signal A[1..N], that is...

It's not entirely obvious what to do with this question, as the denominator does not easily factorise. However, if we realize that $\displaystyle \begin{align*} s^4 + 40\,000 = \left( s^2 \right) ^2 + 200^2 \end{align*}$ it's possible to do a sneaky completion of the square... $\displaystyle...