Fourier transform Definition and 1000 Threads

I am not sure if I am crazy, I am not a mathematician or physicist by training, but I recall doing some work where if I was interested in the limit of a function in "r space" as r-> Infinity I could just use the value of the function in "k-space" at 0 to get the value I was interested in. Is...

Hi guys, I'm a bit embarassed that my first post here is in this section, but I'm taking a Elec. Eng. course abroad, which is out of my confort zone (i'm majoring in automotive eng.) and I'm trying to solve a few model problems. This one in particular deals with the DFT. Anyway:Homework...

I have a feeling this question has a very simple answer, yet I cannot find it anywhere online. Let's say that I have a data set that represents and evenly-spaced sample of a function, taken uniformly over the interval (a,b) \qquad a,b \in \mathbb{Z} I perform a discrete Fourier transform to...

I have been trying to solve the inverse Fourier transform: \int_{-\infty}^{\infty}\left[e^{-j2\pi ft_0}e^{j\theta}\right]e^{j2\pi ft}df I know that the Fourier transform pair says e^{-j2\pi ft_0}e^{j\theta} \leftrightarrow \delta(t-t_0) but the extra phase term e^{j\theta} makes...

Hey I am trying to figure out this easy problem, and I don't know if I am doing this properly or not here's the questions & the work. x(t) = ae^(bt)*u(-t) F[x(t)] = a*integral[(e^bt)*e^(-jwt)*dt] upper bound = 0 lower bound = -infinity = [a*e^(t(b-jw))] / (b-jw) =...

I have raw data in following format Time <-> Ch1 <-> Ch2 <-> Ch3 0.01 <-> 1.6 <-> 1.62 <-> 1.92 0.03 <-> 1.63 <-> 1.62 <-> 1.96 0.05 <-> 1.63 <-> 1.63 <-> 2.04 ...so...

Suppose f \in L^{4/3}(\mathbb{R}^2) and denote its Fourier transform by \mathscr{F}(f). Is it true that the function g:\mathbb{R}^2 \rightarrow \mathbb{C} defined by g(x)=|x|^{-1}\mathscr{F}(f)(x) is in L^{4/3}(\mathbb{R}^2) also? Simply appealing to Hausdorff-Young and Hölder's inequality...

Hey all. On Wiki (http://en.wikipedia.org/wiki/Fourier_transform#Properties_of_the_Fourier_transform) they have some really good pictures explaining the Fourier transform - see the introduction section. The Fourier transform is of an exponentially decaying sinusoid - where the sinusoid...

hi, could someone explain the following statement, please? Why is the real data only shifted, but the Fourier space data is 'wrapped around'? The only difference should be: exp(k*x*2*i*Pi/N) in reals space vs. exp(-k*x*2*i*Pi/N) in Fourier space. Both have a periodicity of N. So why is there...

Homework Statement Show that for a fixed value of \omega that G(\omega)e^{-i\omega t} is the response of the system to the input signal e^{-i\omega t}. (From Roel Snieder's book 'A Guided Tour of Mathematical Methods for the Physical Sciences', pg 233 (Section 15.7, Problem e)) 2. Homework...

Hey, this is my first post, great forum! You've really helped me a lot of times. I have a problem solving an integro-differential equation. It involves a term of the form: integration over [t, +infinity) of f(s)*exp(t-s)ds. I have to solve the equation using Fourier transform, and most of...

Hey, I am looking at the coupling hamiltonian for electrons in an EM field. In particular I'm interested in the inelastic scattering (this isn't the dominant part for inelastic scattering but it's confusing me). The part of the hamiltonian in the time/space domain that I'm interested in is...

Hi there. I have some trouble with this. I have to find the inverse Fourier transform for: \frac{e^{i 6\omega}}{\omega} So I'm using a table, then: F^{-1}\left ( \frac{e^{i 6\omega}}{\omega}\right )=F^{-1}\left ( e^{i 6\omega}\right ) * F^{-1}\left ( \frac{1}{\omega}\right )=2\pi\left[ \delta...

Homework Statement A 8-point data set is transformed with a DFT and the resulting array has values 1,2,3,4,5,6,7,8 was the data set real or complex? why? Homework Equations The Attempt at a Solution kind of confused with this question all i know is the discrete Fourier...

Hi there. I'm starting with the Fourier transforms, and I'm having some trouble with my first exercise on this topic. The problem says: Given f(x)=H(x)-H(x-l) (H(x) is the Heaviside unit step function). a) Consider the odd extension for f and find its Fourier integral representation. b) Using...

I have to show that the Fourier transform of f(t-a) is exp(-iwa)*F(w). Any headstart?

Homework Statement find the Fourier transform of sin(at) Homework Equations The Attempt at a Solution I'm not sure about the solution but it is known that now I tried using the formula of Fourier transform but I couldn't find anything my question is this: can I...

Let the sawtooth function be defined as follows: h(t) = t, 0<t<1, h(t) = 0, elsewhere The problem is two explain the reason for difference between the following two forms of the Fourier transform of h(t), which is denoted as H(f). First method is straightforward, i.e., use the Fourier...

Homework Statement What is the Fourier transform of v.grad(u) Homework Equations The Attempt at a Solution I get i*u(hat)(xi)*v.xi

Hello all. I'm trying to compute the Fourier transform of a square annulus analytically. A "square annulus" would be the square analog of an infinitely thing ring (circular annulus). Here's what I know: The Fourier transform of a circular annulus is a Bessel function. In polar coordinates...

Hi all I know that the Fourier transform of x(t)=1 is X(jω)=2πδ(ω) by using the duality property. This implies: \int_{-\infty }^{+\infty }e^{-j\omega t}dt=2\pi\delta(\omega) Consequently, for ω≠0: \int_{-\infty }^{+\infty }e^{-j\omega t}dt=0 And as a result: \int_{-\infty }^{+\infty...

If f(t) has the Fourier transform F(ω), what is the Fourier transform of the function g(t) = f(3t) − f(4t + 7)? Use the shift property and time scaling property of the Fourier transform to obtain your answer. I have no idea how to start, please help, thanks..

http://imageshack.us/photo/my-images/546/unledho.jpg/ I got the Fourier transform as 2sinc(w) for the first part. How do i do the 2nd part? Thanks.

Homework Statement What is the function f(r) s.t int {d3r.f(r).e-iw.r= 1/w2} where w = (kx,ky,kz) Homework Equations None The Attempt at a Solution I tried to directly take Fourier transform of 1/w2 as \int{ d3r.1/w2.eiw.r}. I started integrating dkx bu calculus of residues, calling the...

Does this ever have meaningful data to it? What are its applications? I am measuring a signal that will have phase-shifted echoes, which means it will have a comb filter waveform multiplied by the original signals Fourier transform because of the phase-shifting. explanation here...

Homework Statement Suppose that f has Fourier transform f(hat). If a is a member of Rn, let g be the function defined by g(x) = f(x-a). Show that g(hat)(xi) = e-i*xi.a * f(hat)(xi). Homework Equations The Attempt at a Solution Is it using the convolution theroem otherwise I am lost.

Fourier Transform -- Completely Flustered About Recursive FFT Hi all. I have been banging my head about this problem for the last week and a half-- Fourier Transform. Some background about me: I am a rising Junior at an accredited university majoring in Computer Engineering & Computer...

Issues with Discrete Fourier Transform in Mathematica Maybe someone else had this problem. Lets say we have a sampled Gaussian pulse in time domain and transform it into frequency domain. For that I use the discrete Fourier transform. Now the resulting set of transformed values is made up of...

Homework Statement Here is a signal \frac{5000}{\pi}sinc^{2}(50t) + \frac{10000}{\pi}sinc^{2}(50t)cos(100t) Find it's Fourier transform and draw it Homework Equations Standard Fourier transformations The Attempt at a Solution Well \frac{5000}{\pi}sinc^{2}(50t) =...

I have an acceleration signal from a wii remote and I am supposed to do an FFT (Fast Fourier Transform) on it, but I don't really understand what it means I get that. I know that a Fourier Transform takes time domain data and Transforms it to Frequency domain but I don't understand what is being...

[Solved] Inverse Fourier Transform Homework Statement If F(\omega)=e^{-|\omega|\alpha}\,(\alpha>0), determine the inverse Fourier transform of F(\omega). The answer is \frac{2\alpha}{x^{2}+\alpha^{2}}Homework Equations Inverse Fourier Transform is defined as...

Homework Statement Use Fourier transform to find the solution of the following differential equation: \frac{\mathrm{d^3}y }{\mathrm{d} x^3}+ \lambda \frac{\mathrm{dy} }{\mathrm{d} x} - xy = 0, \lim_{x \to \infty } y(x)=0 Find the asymptotic of the solution for lambda>> 1. Normalize the...

I need to find the Fourier transform to this function and I'm really stuck, because i tried substituting it into the Fourier transform equations but i started to get a really long integral that got out of hand! i also know that but i don't know how to incorporate it into finding the Fourier...

Hey guys, I was imagining that I have a sine function: y = sin(x) where x represents a distance in meters for instance. Now let us say that I sample the function at x = 0,1,2,3...,10 (meters) producing a list of values: {sin(1), sin(2), sin(3),...,sin(10)} = {0.000, 0.841, 0.909, 0.141...

Homework Statement at t=0, x=0, a schoolboy sets off a stink bomb halfway down a corridor that is long enough to be considered infinite. The dispersion of the particles obey the modified diffusion formula: \frac{\partial \rho (x,t)}{\partial t} - D\frac{\partial^2...

Homework Statement Use the reciprocity relations and known transforms to compute the Fourier Transform of the given function. f(x)=\frac{1}{1+x^{2}} Homework Equations With the help of the table of Fourier transforms, write the given functions as F(f). The Attempt at a Solution...

I'm having trouble following a step in my notes: first off the heat equation is given by: \frac{\partial u}{\partial t}=k^{2}\frac{\partial^{2}u}{\partial x^{2}} then take the Fourier transform of this w.r.t.x, where in this notation the Ftransform of u(x,t) is denoted by U(alpha,t)...

I've never really thought about this before, but today it hit me: Why do we define the Fourier transform of a function to be \hat f(k) = \frac{1}{\sqrt{2 \pi}} \int_{-\infty}^\infty f(x) e^{ikx} dx What do we lose if we just define it to be \hat f(k) = \int_{-\infty}^\infty f(x) e^{ikx} dx

Homework Statement Homework Equations i cannot start with the q The Attempt at a Solution how to find the Fourier transform of the given function? i don't want the MATLAB code, i want to know how to actually find the Fourier transform of this function

Homework Statement Dear all, I have a problem when I using MATLAB to get the Fourier transform of dirac delta function. below is my code.Homework Equations clear all; clc; close all; % t=0:0.002:2; t=0:0.002:4; dt=t(2)-t(1); u=zeros(size(t)); pos0=find(t>=1,1); u(pos0)=1/dt...

Is there a difference? My notes are inconsistent and very poor. Google search doesn't seem to be having much use. Which one transforms into pi(dirac(w+w0) + dirac(w-w0))? Thanks Thomas

Homework Statement The Fourier transform of the auto correlation function is the energy spectral density (ESD) of a signal. Here is the "apparent" proof: \int e^{-jwT} [ \int g(t)g(t+T)dt] dT => \int g(t)[ \int g(T+t)e^{-jwT}dT] dt What happened here? Why did the second integral change from...

Homework Statement Hi, I was wondering why the Fourier transform of 1 is 2\pi\delta(w) I would of though that one would be of infinite frequencies (like a square wave). Further more if g(t) = 1, for all t, g(t) = 1. Why does the Fourier transform have the argument of g(t) = 1 have...

Homework Statement Homework Equations The Attempt at a Solution For part i) I got the answer 1/((jw)^2 + 5jw +6) For part ii) I first consider input to be a unit impulse Thus, Y(w)=H(w)F(w) and F(w)=1 yI(t)=-1/2pi integrate from -infinity to infinity (e^jwt)/(w^2 - 5jw -...

Homework Statement A periodic function of period 2\pi is defined by: f(t)=\frac{t}{2} , 0<t<2\pi Show that the trigonometric Fourier series of f(t) is given by: f(t)=\frac{\pi}{2} - \sum_{n=1}^{\infty} \frac{1}{n}sin(nt) Homework Equations The Attempt at a Solution I've gotten...

Homework Statement Not really a homework question, but related none the less. I'm confused about what exactly the amplitude spectrum is. As well as the power spectrum. Homework Equations Not really taking a purely mathematical approach here, I'm using numpy for python. Specifically the fft...

First of all I apologies if I am in the wrong part of the forum for this question but here it is: How do I go about finding the Fast Fourier Transform (FFT) for a given data set? Homework Equations Ive tried using FFT Magnitude = FFT (Real numbers)^2 + FFT (imaginary numbers)^2...

Homework Statement Can someone tell me how to Fourier transform this quantity: \Sigma (x_(j+1) - x_j)^2 where the sum is from j=1 to N Homework Equations Define the Fourier transform as x_j = \Sigma A_k *exp(-iqkj) **Where i is sqrt(-1) **The Sum is from k=0 to (N-1) **q =...

Is it going from the frequency domain to the time domain? Also, is there a relationship between the Fourier series and transform? Thanks for your help!

Homework Statement find the Fourier transform of complex exponential multiplied to a unit step. given: v(t)=exp(-i*wo*t)*u(t) Homework Equations ∫(v(t)*exp(-i*w*t) dt) from -∞ to +∞ The Attempt at a Solution ∫([v(t)]*exp(-i*w*t) dt) from -∞ to +∞...