Fourier transform Definition and 950 Threads

Hi all, I'm new to Matlab, and I'm trying to evaluate a function via fast Fourier transform using Matlab, then compare the values at each gridpoint with the exact value. The function is y1 = cos(x)-20*sin(5*x)+6*sin(12*x) on the interval [-pi, pi], using n = 9 gridpoints. I first tried...

Trigonometric Polynomials... It's too difficult to understand... Please tell me how a complex trigonometric polynomial works. I think real trigonometric polynomial is good enough. T_{N}=\sum^N_{n=0}a_n cos(nx) +i\sum^N_{n=0}a_n*sin(nx) T_{N} is postion at time x of an object moving along a...

Hi, I am very new to Matlab, and I'm supposed to use the built-in FFT function to do discrete Fourier Transform for f(x) = sin x + 4 cos(5x) + (sin(6x))^2 on the interval [-pi, pi] with a uniform partition for the interval with n = 9. Then I have to (a) Plot the magnitudes of the Fourier...

Hi, I'm using the following definition for the Fourier transform. F\left( q \right) = \int\limits_{ - \infty }^\infty {e^{iqx} f\left( x \right)dx} (I used a capital F instead of f with a squiggle on top because the tex code doesn't seem to be working the way I intended it to.) I...

Hello everyone ^^ Why I can say "The Fourier transform tells us " how much sinusoid" there is in the waveform at a given frequency "w"" Form Linear circuit analysis by Artice M. David thanks a lot

Im trying to get the Fourier transform of x(t)=u(t)-u(t-1) from what i know the FT of u(t) is pi*delta(omega)+1/jw so for the u(t-1) would we have to use the time shifting property of Fourier transforms so that it becomes pi*delta(omega)+1/jw*(exp(-jw_o)??

:rolleyes: :cool: I have a question..yesterday at Wikipedia i heard about the "Hermite Polynomials2 as Eigenfunctions of Fourier (complex?) transform with Eigenvalues i^{n} and i^{-n}...could someone explain what it refers with that?...when it says "Eigenfunctions-values" it refers to the...

I am given this signal: x(t) = sin(4(t-1)) and I need to find X(jw), i.e. it's FT, so I am confused whether I shift by 1 or by 4, in other words whether I multiply F{sin(4t)} by e^(4jw) or by e^(1jw) which one is it? I am thinking it's 4jw... is it right?

Hi, I'm solving an exercise in optics (Fraunhofer diffraction) and reached a mathematical difficulty - I need to find the Fourier transform of a phase function, of the form exp[-i f(x)]. I can't seem to be able to do this. I have an idea that the result should be a series of delta functions...

I'm trying to uniquely determine a complex function given pairs of real valued functions derived from it. For example, if you have its real and imaginary parts, or phase and the magnitude, the function is uniquely determined from them. But what if you have the magnitude of the function and...

Find the solution (in integral form) of the equation: u(x+1,t) - 2u(x,t) + u(x-1,t) = u_t u(x,0) = f(x) Hint: Use the shift formula F[f(ax-b)] = \frac{\exp{i\omega b/a}}{|a|} \overline{f}(\omega/a) So I took the Fourier transform of each term using the shift formula: \exp{(-i\omega)}...

If we define the function: F[w]=\int_{-\infty}^{\infty}dxe^{-iwx}g(x) my question is..what would be the criterion to decide if F[w] has all the roots real (w=w*) and how is derived?..thanks.

Hi, how do I find the Fourier transform of this function sin x / x, i.e., f* = Integral( sin x / x * exp( i*w*x) dx from -infinity to +infinity ). I've been using Jordan's Lemma up to this point, but it doesn't seem to apply here as a way to evaluate the integral. Thanks for any help.

What are the differences? I mean when we will make a decision "hmm now i must use laplace transform or now i must use Fourier transform". What are the absences in laplace transform so Fourier design a new transfom? I want to know these transforms' main idea, differences. I am looking...

Hi, I want to know how to get rid of the time part of the homogeneous wave equation: \newcommand{\pd}[3]{ \frac{ \partial^{#3}{#1} }{ \partial {#2}^{#3} } } \nabla^2\psi-c^{-2}\pd{\psi}{t}{2} = 0 I've read that this can be done using a Fourier transform, with the following given as the...

suppose we have this discreet function: x(k)=rect(k+N/2)= 1 ; when -N/2=<K<=N/2-1 x(k)=0; otherwise This is discreet function(not continuous) of k shifted forward by N/2, we need to find Fourier transform for it .. anyway let N=6 for simplicity, then: x(k)=rect(k+3)= 1 ; when...

Here's my problem: I've got the Fourier transform of f(x) as F(K) = \frac{1}{\sqrt{2\pi}} \int\limits_{-\infty}^\infty f(x) e^{-ikx} dx Likewise for g(x) I have G(K) = \frac{1}{\sqrt{2\pi}} \int\limits_{-\infty}^\infty g(x) e^{-ikx} dx for F(K/lambda) I have F(K/\lambda) =...

Fourier transform --> power spectrum Hey all! I've been learning about the discrete Fourier transform (and FFT too) recently. What I don't understand is why applying it to a signal gives its power spectrum. I am not really good in physics, so to me it just seems like a magical formulae, one...

ok so here's the question, show explicitly that the integral from -inf to inf of |f(k)|^2=1 where f(x) = \frac{N}{\sqrt{\sigma}}*e^{\frac{-x^2}{2\sigma^2}} When doing the integral for the forier transform, I was going to use the gaussian integral to simplify it, but I don't htink I can do...

I am trying to solve this Fourier problem where I have to integrate ∫f(x) * exp(-i§x) dx from -∞ to ∞ , where f(x) = exp(-sgn(x)) I tried breaking the function into two pieces where x is from -∞ to 0 and from 0 to ∞ where f(x) would then be exp(x) and exp(-x) and integrating two functions...

Can someone help me out in understanding this Fourier Transform and how can it be applied to different situations? Any Useful links or information would be highly appreciated. Regards, FuRy

I want to take an audio recording of a sound, perform a Fourier Transform on this sound, and then use the amplitude/frequency/phase information provided by this transform to set the amplitude/frequency/phase of an set of sine wave oscillators, in order to resynthesize the sound. I need to know...

how can I calculate the Fourier transform for unit step function: v(t)=1 where 0=<t<+infinity v(t)=0 otherwise I applied the general definition relation for FT: v(w)=integral(v(t)*e^-jwt) ; - infinity<t<+infinity but i had v(w)=infinity due to the term infinity-displaced e^(+jwt)...

let us asuume this discrete signal: f(n)=a^n * u(n) ; where u(n) is unit step function ; u(n)=1 where n>=0 u(n)=0 where n<0 ;0=<a<1 and the foruier transform for discrete signals is defined as : F(i)=sum (...

e^{-x^2}\cos \left( e^{x^2} \right) Mathematica doesn't have an algorithm for it, does a closed form exist for the Fourier transform? It's continuously differentiable on all intervals in R, and it converges to zero at the infinities (the derivative blows up there).

I want to solve the partial differential equation \Delta f(r,z) = f(r,z) - e^{-(\alpha r^2 + \beta z^2)} where \Delta is the laplacian operator and \alpha, \beta > 0 In full cylindrical symmetry, this becomes \frac{\partial_r f}{r} + \partial^2_rf + \partial^2_z f = f - e^{-(\alpha r^2 +...

For the function f(x) given by: f(x) = e^{2x} (x<0), = e^{-x} (x>0) I have got the complex Fourier Transform to be: F(k) = {3(k^{2} + ik + 2)}/{(k^{2}+1)(k^{2} + 4)} Now I'm trying to verify the formula for the inverse transform by using a D-contour integral. Just taking the x>0 case I...

How can I prove that doing a Fourier transform on a function f(x) twice gives back f(-x)? Thanks..

we need to find the F.T of f(t) = 0 for t<0 f(t) = exp(-at) for t>=0 where a is a real positive constant and F(w) = the integral w.r.t t between minus infinity and plus infinity of [exp(iwt)*f(t)] which turns out to be 1/(a-iw) we now have the ODE L*dI/dt + RI = f(t) where L,R are...

Let be the function Ln\zeta(2e^{-s}) does its Fourier transform exist?...where \zeta(s) is teh Zeta function of Riemann...

I do not know how to transform a Fourier transform integral in S^3 by a Hopf fibration to S^2. I have the three variables (r,theta ,phi) in spherical polar coordinate,S^2 and (r,theta,phi and psi) for S^3 where psi:[0..4*pi ]and theta:[0..pi ]and phi:[0..2*pi].

Hi, Sorry about the text, but Latex doesn't work. Can anyone please give me an outline for the derivation of the probability function by inverting its Fourier transform, i.e. P(X>x) = \frac{1}{2} + \frac{1}{\pi} \int_{0}^{\infty} Re \bigg[\frac{e^{-i \theta x}f(\theta)}{i \theta} \bigg]...

Hi, I got an exam in calculus in a few weeks, and lots of questions coming up. Here's one of them: We learned that the Fourier Transform of f(x) = e^{-|x|} is \hat f(\omega) = \sqrt{\frac{2}{\pi}}\frac{1}{1+\omega^2} I've got no problem with this one. Now, since \hat f(\omega)...

Hi there, I have a range of results from scanning a piece of metal of length L. The results from the scan are %FSH of the oscilloscope. I have to analyse the noise of the signal and thought I'd do this using a Fourier transform. Using the range of results as follows could you please tell me...

I'm trying to justify to myself that the inverse Fourier transform of the Fourier transform of a function is the function itself, provided that the FT exists. I can't simplify the double integral that results when this operation is performed, and much to my dismay, nothing at Mathworld...

Hello there, Im sure someone on this forum must know how to go about this. It is part of an exam question. Firstly I must draw a sketch of this pulse: v=0 when |t| > a v=V0( 1 + t/a ) when -a < t <= 0 v=V0( 1 - t/a ) when 0 < t < a v represents amplitude, V0 represents peak...

I need to show the solution to the Fourier transfor of f(theta) = |sin(theta)|. However i think that solving this needs to be done by complex anaylsis as integration by parts just keeps going on and on. Does anyone know where to go with this?

Mathematica can't calculate Fourier transform (Dirac mean position eigenfunction) Hi, I'm attempting to use Mathematica to calculate a mean-position eigenfunction of the Dirac equation. To do so I need to evaluate Fourier transforms (from p-space to r-space) of wavefunctions dependent on...

Hi all , This FFT program may help some of you in your Engineering studies , it was a lot of fun to write and use .. I wrote it in pascal . All the instructions are included at the beginning.. I think my approach to reordering the twiddle factors is innovative as it is written in assembly...

Last year I made a more modern version of a QM simulation I did a long long time ago, It makes movies of time evolutions of arbitrary wave functions in a QM harmonical oscillator. (You can see the movies via the links below) http://www.chip-architect.com/physics/gaussian.avi...

Why is it that the Fourier transform of e^{2\pi ikx} is equal to \delta(k) ? The delta function is supposed to be zero except at one point. But the integral doesn't converge for k \ne 0 . Yet I see a lot of books on QFT use this identity.

Hello Listmembers, I am trying to make some progress in my understanding of Schrodinger's equation.I have been trying to teach myself about Fourier transforms in the hope that this will help me understand the derivation of Schrodinger's equation. My question has to do with slide number...

hi , the question is to find the Fourier transform of the following eqn without using integration d(t)= [c(-1.5t)]exp(jwat) where c(t)= Ao + E(Sumation)An*cos(nwot) + Bn sin(nwot) [fourier series formula] I knwo to find the FT of the above Fourier series. But why is exp(jwat)...

Mathematically, these are three distinct, although related beasts. Laplace transform (function f(x) defined from 0 to inf) integral of f(x)e-xt, defined for t>=0. Fourier transform (function f(x) defined from -inf to inf) integral of f(x)e-itx defined for all real t. Complex Fourier series...

In an assignment, I've been given a function: x(t) = \theta(t-t_1) - \theta(t-t_2) Assume t_2 > t_1 and we are asked to find the Fourier transform. So I wrote down: x(\omega) = \int_{-\infty}^{\infty}{e^{-i\omega t} [\theta(t-t_1) - \theta(t-t_2)] dt} I know that the...

hi, there hope someone can help me the task is simple, i have to calculate the Fourier tranform of wave-function to get it in momentum space the problem is that this is a 4-dimensional space, so the Fourier transform is multi-dimensional the only idea i have is that this...

Hi All, I've been going through a few Fourier transform problems and I'm stuck with integrating this one: f(x) = e^(-pi*x^2) then F(e^(-pi*x^2)) = integral (e^(-pi*x^2) * e^(-i*w*x)).dx Can anyone help me out? Many Thanks, Pete

Hi all, I had this problem for homework and it stumped me. It's too late to get points for it, but I'd like to know for future reference. I posted in the homework help forum but figured I'd try here too. Find the Fourier transform F(w)=integral from -infinity to infinity of f(t)e^(i*w*t)dt...

Hi all, I had this problem for homework and it stumped me. It's too late to get points for it, but I'd like to know for future reference. Find the Fourier transform F(w)=integral from -infinity to infinity of f(t)e^(i*w*t)dt f(t)=e^(-t^2/a^2) i=sqrt(-1) w=omega=constant a=constant...

please refer to the attachment. what is the physical meaning of g(k)?