Transform Definition and 1000 Threads

Homework Statement Determine Fourier Transform of f(t) = cos^2 ω_p t ... for |t|<T also, for |t|>T, f(x) = 0, although i don't think you need to do anything with that. The Attempt at a Solution okay so: f(t) = cos^2 ω_p t ... for |t|<T becomes f(t) =...

Homework Statement I am using the time differentiation property to find the Fourier transform of the following function: Homework Equations f(t)=2r(t)-2r(t-1)-2u(t-2) The Attempt at a Solution f'(t)=2u(t)-2u(t-1)-2δ(t-2) f''(t)=2δ(t)-2δ(t-1)-?? Can somebody explain what the...

hi I know the Fourier transform of a lorentzian function is a lorentzian but i was wondering if the Fourier transform of the second derivation of a lorentzian function is also a second derivative of a lorentzian function Thanks

Hi all, I've been trying to solve the following I = \int_{-\infty}^{\infty}\int_{-\infty}^{\infty} \frac{x}{(x^2+y^2+d^2)^{\frac{5}{2}}} e^{-i(kx+\ell y)} \ dx \ dy where d,k,\ell are constants. I haven't been able to put this into a tractable analytic form and I figured I'd consult all...

Hey Physics Forums, Grading an assignment, the current topic is continuous Fourier Transforms. They're trying to prove the convenient property: \mathcal{F} \left[ \frac{d^n}{dx^n} f(x) \right] = (i \omega)^n \mathcal{F} \left[ f(x) \right] So there's a simple way to get it: Let f(x) be...

Homework Statement This is copied from a book: $$\eqalign{ & {\rm{Time Differentitation}} \cr & {\rm{Given that: }}F(\omega ) = F\left[ {f(t)} \right] \cr & F\left[ {f'(t)} \right] = jwF(\omega ) \cr & {\rm{Proof:}} \cr & f(t) = {F^{ - 1}}\left[ {F\left( \omega \right)}...

Hi, I am having a little trouble with the physical meaning of a Fourier transform. I will try to pose a concrete example. Mathematically, the Fourier transform of an exponential decay results in a Lorentzian function. Let's say I have a population that decays exponentially with time. Now, if...

Hi guys~ I have got a few things about some Fourier transform Q/A that i wanted to check...so here you go: 1) Find the Fourier sine and cosine transform of f(x)=x 0<x<3 ok, for the sine, i get -9/n∏ but i get zero for cosine part, is it wrong? and the second one: find the Fourier transform...

Hi guys :) I'm looking to get a jump start on my uni course and have been going through some topics on my own before classes start in the Fall, I've reached the point of Laplace Transform and Fourier maths - and it's tough! I have a small question on an inverse laplace transform equation in...

I originally asked this in the Calculus & Analysis forum. But perhaps this is better suited as a question in Abstract algebra. For the set of all Dirac delta functions that have a difference for an argument, we have the property that: \int_{ - \infty }^\infty {{\rm{\delta (x -...

I just started reading a pamphlet written my an M.D. about a poorly understood illness. On the second page he writes: "Hypoxia is a technical term meaning the inability to transform oxygen into energy." On the next page he writes: "It is due to a problem at the cellular level converting...

Changes in the internal structure during a "Topological transform" Is there any field of topology which deals with the changes in internal structure of an object when it undergoes topological transform? If I'm transforming a cube into a sphere, is there any 'field of topology' which analyze the...

Dear fellow physicists, looking at the derivation for the maxwell equations into k-space, I've stumbled upon something that seems not so logical to me. It is concerning the two parts where they transform \nabla \times E and \nabla \bullet E on page 27 (on the sheets 14)...

Hello all, Assume we have an optimization problem and that strong duality holds. Will it also hold for another optimization problem obtained from the initial by a bijective coordinates transform? Thank you in advance.

Hi, Part of my research, I nondimensionalized an ODE to eventually arrive at this form: sin(τλ) = q^((n+2)/(n+1)) + κq' + q'' where q' = dq/dτ The problem is of course the nonlinear q^n. n is an integer greater than 0. Is there a Laplace transform for this? Or what solutions are there for...

Hi there, I have a little problem in wave optics: I have a wave function \psi_{ap} that depends on some geometric parameters, but that has no units itself (as one would expect). But unfortunately when I calculate the Fourier transform of this wave function the Fourier transform has a unit...

Hello again. First off, I wasn't sure how to say this in the title but I'm not taking the inverse Laplace transform of a unit step function. I'm taking the Laplace transform of something that comes out to the unit step function. I have this question, which is a similar version of the...

... C1.... C2-> P-> In the above illustration, P is a particle, C1 and C2 are detectors able to measure the energy/mass of a light pulse. C1 is at rest, P and C2 move horizontally to right with the same velocity. Let's say that P is actually a matter-antimatter pair that annihilates to...

Consider one-sided Laplace transform:$$\mathcal{L} \left \{ h(t) \right \}=\int_{0^-}^{\infty}h(t)e^{-st}dt$$ Q. Is this defined only for the functions of the form f(t)u(t)? If no, then f(t)u(t) and f(t)u(t)+g(t)u(-t-1) are two different functions with the same Laplace transform, and thus...

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Homework Statement How to find the transformation matrix of Object B in world coordinates, when you know the transformation matrix of Object A in world coordinates and the matrix of Object B in Object A's local coordinates Please help!

So I keep hearing that the maxwell equations are variant under Galilean transform. Tired of simply accepting it without seeing the maths, I decided to do the transformation on my own. To make things easy, I only tried Gauss' law, furthermore I constricted the field to the x-axis only. So I have...

Homework Statement Solve y'' + y = f(t), y(0)=0, y'(0)=1, f(t)= (0 for 0<t<pi) (1 for pi<t<2pi) (0 for t>2pi) The Attempt at a Solution y'' + y = upi(t)-u2pi(t) s2L{y} -sy(0) -y'(0) +L{y} = L{upi(t)} -Lu2pi(t)} L{y}(s2+1) -1 = (e-pi*s/s) -(e-2pi*s/s) L{y} =...

If you take the absolute value of the FFT output, does that give you the amplitude? I am asking because I have seen example where that is taken as the amplitude, and examples were the absolute value is multiplied by either SQRT2 or by 2 to get the magnitude. So my question is what is...

Homework Statement Find laplace trasform of g(t) g(t) = 0 for 0<t<1, t^2 for t>1 So this can be re-written as g(t) = t2*u1(t), where u is the unit step function. By using the fact that L(uc(t)f(t-c)) = e-csF(s) i am trying to take the laplace... So in this case, f(t-c) = t2 ... so then does...

!Euler transform matrix multiplication help! Homework Statement This may be rather simple but i am really struggling to complete a 3 3x3 matrix multiplication. I NEED STEP BY STEP WORKING!. This would really help me I understand the theory. Basically I have three matrices T1= cosψ sin ψ...

Multi-Variable / Dimension Fourier Decomposition Say we have f(x, y). We can Fourier decompose it in terms of f1(y, v) and e^{\ x\ v}, f2(x, u) and e^{\ u\ y}, or both variables simultaneously f3(u, v) and e^{\ x\ v\ +\ u\ y}. Similarly for any greater number of variables or dimensions. Now, is...

Hi I am looking for free software that can transform Word Doc to PDF. Maybe PDF back to Word Doc. Any suggestion on which one is good? Thanks Alan

Hi, I know this topic is more suited for Computing & Technology, but it has even more to do with general questions about Fourier transform capabilities. I have a question about sample restoration in Discrete Fourier Transform. Suppose we have a signal with the stack of frequencies from 1 Hz...

Homework Statement The Attempt at a Solution I don't understand this step. It's got to be some sort of identity that I missed. I also don't understand why the limits of integration change.

Fourier Transform help! (bit urgent) Hi there, I'm having a recurring problem with my Fourier transforms that I have tried really hard to figure out but I feel like I'm missing something important. It keeps popping up in my communications and signal processing papers. I keep getting FTs...

OK, I've found a great explanation of the derivation of the Lorentz transformation, with x' = γ [ x - v t ] t' = γ [ t - ( v / c2 ) x ] so if I take the other term as 0, there is x'( t = 0 ) = γ x t'( x = 0 ) = γ t but the problem is that the time dilation & length...

I understand that if you have a system that is linear and time invariant, that you can perform a Fourier transform on it. But that doesn't mean you need to Fourier transform it. Or does it? Is a linear, time invariant system equivalent to or in some way implies a Fourier transform? Or is the...

Homework Statement Is there an easier way of solving this rather than doing the integral? Find the laplace transform of: t{e^{ - t}}u(t - 1) Homework Equations The Attempt at a Solution \int_1^\infty {t{e^{ - t}}} {e^{ - st}}dt = \int_1^\infty {t{e^{ - t(1 + s)}}} dt =...

Homework Statement I am attempting to perform a z-transformation on the terms 1/(z-3) and 1/(z-5) but I cannot find a sequence which fits this form in any of my tables. Is there a transform for these terms or do you just leave them as they are? Homework Equations The Attempt at a...

Hi, I'm reading a book called Robotics, written by Tadej Bajd on my own to learn about robotics and have no one else to put my questions other than to the forums. Here the writer on 11th page writes: "By considering the similarity of triangles in Figure 2.3, it is not difficult to derive...

Homework Statement F{f(t)} is the Fourier transform of f(t) and L{f(t)} is the Laplace transform of f(t) why F{f(t)} = L{f(t)} where s = jw in L{f(t)} The Attempt at a Solution I suppose the definition of F{f(t)} is ∫[f(t)e^-jwt]dt where the lower integral limit is -∞...

Just began a serious study of the Fourier transform with a couple of books. One of them defines the Fourier transform on \mathbb R as \hat f(\xi) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^\infty f(x) e^{-i\xi x}dx. Another defines it as \hat f(\xi) = \int_{-\infty}^\infty f(x)...

Homework Statement I need to solve the ODE y''-y = t - tH(t-1); y(0)=y'(0)=0 Homework Equations - The Attempt at a Solution I'm fine with the process of solving the ODE, but I need a little help regarding the first t. From what I understand from lectures, all of the 't' terms need to be in...

I'm trying to evaluate the following intergral using complex function theory: \begin{equation} \int_{-\infty}^{\infty}\int_{-\infty}^{\infty}\frac{e^{i(ap+aq+b\sqrt{k^2-p^2-q^2})}}{\sqrt{k^2-p^2-q^2}}dpdq \end{equation}I though that it is possible if i can calculate: \begin{equation}...

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Homework Statement The Attempt at a Solution I can't get the jump to [e^-st(-s cost bt + b sin bt)]/(s^2+b^2) They say they have to use integration by parts but when e and a trig ratio are involved that requires tabular integration. They're obviously not using tabular...

Homework Statement The Attempt at a Solution I can understand step 2 to 3, but I can't get step 1 to 2. For simplicity sake we'll just call e^(3-s)t = N since it will = N anyway ultimately. I think the answer should be [N/3-s - 1/(3-s)^2)N - (0 - 1/(3-s)^2)0 The second term...

Hi, First, I would like to ask for your apologize for my very bad english... My name is Frédéric Serrano, I'm a technician and I'm starting my own business. For a new contract my customer ask me to adapt his industrial machine for the USA. So I have to comeback to the basic rule. Here in...

We know that the \mathcal L\{f(t)\} = \int^{\infty}_0 e^{-st}f(t) dt. Say we want to, for example, solve the following IVP: y'' + y = f(t) where f(t) = \begin{cases} 0 & 0 \leq t < \pi \\ 1 & \pi \leq t < 2\pi\\ 0 & 2\pi \leq t \end{cases} and y(0) = 0 , y'(0) = 0 We apply Laplace on both...

If you Lorentz transform a scalar: U^{-1}(\Lambda)\phi(x)U(\Lambda)=\phi(\Lambda^{-1}x) If you now perform another Lorentz transform, would it it look like this: U^{-1}(\Lambda')U^{-1}(\Lambda)\phi(x)U(\Lambda)U(\Lambda')=\phi(\Lambda'^{-1}\Lambda^{-1}x) ? But isn't this wrong...

I guess this is programming and physics all combined into one but hopefully I can get some help anyway. I am doing some signal analysis of real-time streaming sensor data. I would like to do a DFFT on the data in real time as it streams in. So far pretty easy, however, there are a number of...

Hi I am trying to analytically calculate the Fourier transform attached. I am getting really stuck with the integral, can anyone help? I've attached how far I've got with it, any help much appreciated! Kind Regards, Mike

the questions are together with this file and my solutions are also attached. hope someone can comment on my solutions. thanks a lot and i hope i won't get any warning any more.

Hi, I was given the attached question and have given my wrong attempt at the answer. I know how to work the answer out (also shown) but I would like to know why my first attempt is wrong. Many Thanks