Fourier transform Definition and 950 Threads

Okay I have a question involving calculating the FFT of a signal from a sensor. I have simulated many different scenarios in MATLAB of various noise characteristics involving the signal. I want to take the FFT of a noisy signal. As long as my expected input signal has a higher amplitude than...

Homework Statement Given x[n] with transform X(ejw), find the Fourier transform in terms of X(ejw). x1[n]=[0.9ncos(0.6*pi*n)] * x[n-2] Homework Equations time shift: x[n-k] -> e-jwkX(ejw) convolution: x[n] * h[n] -> X(w)H(w) freq. shift: x[n]ejwcn -> X(ew-wc) The Attempt at a Solution I...

Hi PF! I was wondering if you could clarify something for me. Specifically, I am solving the heat equation ##u_t = u_{xx}## subject to ##| u(\pm \infty , t ) | < \infty##. Now this implies a solution of sines and cosines times an exponential. Since we have a linear PDE, we may superimpose each...

Homework Statement I am given f(t) = e^-|t| and I found that F(w) = ##\sqrt{\frac{2}{\pi}}\frac{1}{w^2 + 1}## The question says to use the nth derivative property of the Fourier transform to find the Fourier transform of sgn(t)f(t), and gives a hint: "take the derivative of e^-|t|" I also...

I have recorded a micrograph of a 2-D array at a magnification of 43,000x on my DE-20 digital camera, which has a 6.4 μm pixel size and a frame size of 5120 × 3840 pixels. This magnification is correct at the position of the camera. I then compute the Fourier transform of the image. What is the...

Is there a relationship between amplitude and phase response of a realizable filter? For the purpose of ease, let us consider only a FIR digital filter. I would like to design a FIR digital filter with a given frequency response (amplitude and phase responses given as a function of frequency)...

Below is my walkthrough of a Fourier transform. My problem is that I want to do all the similar steps for a Fourier transform between position x and the wave vector k. That is working on a solution of the maxwell equations. The maxwell equations has many possible solutions for example: $$...

Homework Statement Homework EquationsThe Attempt at a Solution I tried to attempt the question but I am not sure how to start it, at least for part (i). My biggest question, I think, is how does the multiplication of a random complex number to a Fourier-Transformed signal (V(f)) have an...

Homework Statement Homework Equations The Attempt at a Solution I did Fourier transform directly to the eigenvalue equation and got Psi(p)=a*Psi(0)/(p^2/2m-E) But the rest, I don't even know where to start. Any opinion guys?

Hi Folks, The Fourier Cosine Transform of cos(x) for 0<x<a and 0 everywhere else is given as F(\omega)=\displaystyle\frac{1}{\sqrt{2 \pi}}[\frac{\sin a (1-\omega)}{1-\omega}+\frac{\sin a (1+\omega)}{1+\omega}] I can plot this and we get a continuous amlitude spectrum of F(\omega) against...

Homework Statement Noting that J_0(k) is an even function of k, use the result of part (a) to obtain the Fourier transform of the Bessel function J_0(x). Homework Equations In (a) I am asked to show that the Fourier transform of f(x)=\dfrac{1}{\sqrt{1-x^{2}}} is...

Hi To properly understand introductory quantum mechanics, I want to understand what the Fourier transform actually gives me mathematically. What book do you recommend? I found one book, but it doesn't get to Fourier transformations until after seven long chapters. Is that what I have to expect...

So I have been away from education for a little while now and I'm going through some refresher stuff - in particular I have been playing around with FFTs. If i take (with MATLAB notation): time = 0:0.01:10 y = fft(sin(2*pi*f*time)) with f = 5 then the maximum amplitude of the fft output is...

Homework Statement This comes up in the context of Poisson's equation Solve for ##\mathbf{x} \in \mathbb{R}^n ## $$ \nabla^2 G(\mathbf{x}) = \delta(\mathbf{x})$$ Homework Equations $$\int_0^\pi \sin\theta e^{ikr \cos\theta}\mathop{dk} = \int_{-1}^1 e^{ikr \cos\theta}\mathop{d\cos \theta }$$...

Hi, I've been reading a paper on renormalisation theory as applied to a simple one-particle Coulombic system with a short-range potential. In the process of renormalisation, the authors introduce an ultraviolet cutoff into the Coulomb potential through its Fourier transform: ## \frac{1}{r}...

I'm recently new to the field of 2D Fourier Transform Infrared Spectroscopy and am learning its applications. I would like to know its applications in biology. Specifically, is there anything in the 400 nm to 1000 nm range that is important in protein structure, protein dynamics or biology in...

Alright guys. First off, this is my first post (happy to be here!) and I'm hoping this is the correct section of the forum. I'm an engineering student, currently working towards finishing my master's thesis. Short introduction. I am trying to simulate an ocean wave environment, as a...

I'm asked to transform y(t) = x(t)*x(t) (where * is the convolution product) and x(t)= sinc(t)cos(2π10t) ( sinc(t)= sin(πt)/(πt) ).The attempt at a solution Clearly everything is simple if you know X(f), because y(t)=InverseFourier{ X(f)2 }. The problem is that I can't find X(f). By the way...

Hi, friends! In order to find an orthogonal basis of eigenvectors of the Fourier transform operator ##F : L_2(\mathbb{R})\to L_2(\mathbb{R}),f\mapsto\lim_{N\to\infty}\int_{[-N,N]}f(x)e^{-i\lambda x}d\mu_x## for Euclidean separable space ##L_2(\mathbb{R})##, so that ##F## would be represented by...

Homework Statement A damped harmonic oscillator is driven by a force of the form f(t)=h(t) t^2 Exp(-t), where h(t) is a Heaviside step function. The Oscillator satisfies the equation x''+2x'+4x=f(t). Use pencil-and-paper methods involving Fourier transforms and inverse transforms to find the...

Homework Statement Using a theorem (state which theorem you are using and give the formula), Calculate the Fourier Transform of 1. rect(x)triangle(x) 2.cos(pi*x)sinc(x) 3.rect(x)exp(-pi*x^2) 4.sinc(x)sin(pi*x) 5. exp(-pi*x^2)cos(pi*x) Homework Equations not sure what theorem to use for the...

I am computing matrix elements of a two body quantum-mechanical potential, which take the form V_{k l m n} = \int d^3 r_1 d^3 r_2 e^{-i k \cdot r_1} e^{-i l \cdot r_2} V( | r_1-r_2 | ) e^{i m \cdot r_1} e^{i n \cdot r_2} To do this integral, I make the change of coordinates...

Homework Statement Find the inverse Fourier transform of X(ejw = 1/(1-ae-jw)2 using the convolution theorem. Homework EquationsThe Attempt at a Solution I tried finding the partial fraction coefficients but without success.

Hello, everybody. I am currently working on deriving solutions for Stokes flows. I encounter a multidimensional inverse Fourier transform. I already known the Fourier transform of the pressure field: \tilde{p}=-\frac{i}{{{k}^{2}}}\mathbf{F}\centerdot \mathbf{k} where i is the imaginary unit...

Any books on Fourier transforms and other transformations? (Thanks, for any help)

Hello, I hope somebody can help me with this. 1. Homework Statement I am supposed to show that if there is a function \phi(x,t) which is real, satisfies a linear wave equation and which satisfies \phi(x,0)=0 for x<0 then the Fourier Transform \tilde{\phi}(k) of \phi(x,0) is in the lower...

Can anyone point me to some material on applying the Fourier transform to the case of an analytic function of one complex variable? I've tried to generalize it myself, but I want to see if I'm overlooking some important things. I've started by writing the analytic function with u + iv where u...

we have a wavefunction \psi (x) the question asks for \psi (p) and says to use this to calculate the expectation value of momentum. The problem is the expectation value of momentum is integrated over dx so after transforming how do you get the integral to be over dp? thanks for any help with...

Hi Folks, I need to evaluate the following function f(t)=A[1+B \cos(\omega_1 t+ \phi)] \cos(\omega_2 t+ \phi) to find f(\omega) using the Fourier transform. Ie, the Fourier transform I use is f(\omega)=\displaystyle \frac{1}{\sqrt {2 \pi}} \int^{\infty}_{-\infty} f(t) (\cos \omega t+ j \sin...

Hi everyone, do you know how to calculate the Fourier transform for the infinitely deep circular well (confined system)? The radial wave function is given by R=N_m J_m (k r). k=\alpha_{mn}/R. R is the radius of the circular well. R(k R)=0. Thanks. Another question is that The k in J_{m}(k r)...

Hi, I have a simple harmonic oscillation problem whose Green function is given by $$\Bigl[\frac {d^2}{dt^2}+ \omega_{0}^{2}\Bigl] G(t, t') = \delta(t-t')$$ Now I found out the Fourier transform of $G(t, t')$ to be $$G(\omega)= \frac{1}{2\pi} \frac{1}{\omega_{0}^{2}-\omega^2}$$ which has poles...

Hello, Let's suppose we are given a function f:\mathbb{R}\rightarrow \mathbb{R}, and we assume its Fourier transform F=\mathcal{F}(f) exists and has compact support. What sufficient condition could we impose on f, in order to be sure that F is also bounded?

Whais is the effect of a multiplication by (-1)^n in the DTFT ?? In other words, what's is this transform : x(n)* (-1)^n ??

Hi, I am totally a non-math guy. I had to attend a training (on automobile noise signals) that had a session discussed about Fourier Transform (FT). Let me pl. write down what I understand: "The noise signal observed at any point in the transmission line can be formed using a sum of many sine...

Homework Statement Silly question, but I can't seem to figure out why, in e.g. Peskin and Schroeder or Ryder's QFT, the Fourier transform of the (quantized) real scalar field \phi(x) is written as \phi (x) = \int \frac{d^3k}{(2\pi)^3 2k_0} \left( a(k)e^{-ik \cdot x} + a^{\dagger}(k)e^{ik...

I have been given this y(t)=\frac{sin(200πt)}{πt} All I want is to find, is how the rectangular pulse will look like if I take the transformation of the above. That "200" kind of confusing me, because it isn't a simple sinc(t)=\frac{sin(πt)}{πt} I need somehow to find the height of the...

Hi! I am taking a second look on Fourier transforms. While I am specifically asking about the shape of the Fourier transform, I'd appreciate if you guys could also proof-read the question below as well, as I've written down allot of assumptions that I've gained, which might be wrong. OK...

Hi bros, so I feel like I am very close, but cannot find out how to go further. Q.1 Compute the DTFT of the following signals, either directly or using its properties (below a is a fixed constant |a| < 1): for $x_n = a^n \cos(\lambda_0 n)u_n$ where $\lambda_0 \in (0, \pi)$ and $u_n$ is the...

Hi, My aim is to get a series of images in 2D space that run over different timestamps and put them through a 3D Fourier Transform. So my 3D FT has 2 spatial axes and one temporal axis. However I have never done anything like this before, and I have a very basic knowledge of Python. So...

Homework Statement OK, we're given to practice Fourier transforms. We are given f(x) = \int^{+\infty}_{-\infty} g(k) e^{ikx}dk and told to get a Fourier transform of the following, and find g(k): f(x) = e^{-ax^2} and f(x) = e^{-ax^2-bx} Homework Equations The Attempt at a Solution For...

Is there a time domain function whose Fourier transform is the Dirac delta with no harmonics? I.e. a single frequency impulse

I have this expression: f(\tau) = 4 \pi \int \omega ^2 P_2[\cos (\omega \tau)] P(\omega) \, \mathrm{d}w \quad [1] where P_2 is a second order Legendre polynomial, and P(\omega) is some distribution function. Now I am told that, given a data set of f(\tau), I can solve for P(\omega) by either...

When I sample a certain digital signal with increasing sampling frequency, the fast Fourier transform of the sampled signal becomes finer and finer. (the image follows) Previously I thought higher sampling frequency makes the sampled signal more similar to the original one, so the Fourier...

Hi All, I have a problem I've been thinking about for a while, but I haven't come up with a really satisfactory solution: I want to do a discrete Fourier transform on data that has been sampled at 2 different sampling frequencies. I've attached a picture of what my data will look like...

Homework Statement Find the FT of the following signal The function is: f(t) = t(\frac{sen(t)}{t\pi})^2 Homework Equations Fourier transform: F(\omega)= \int_{-\infty}^\infty f(t)e^{-jt\omega} My attempt began with this Fourier transform, and that's my goal: F[tf(t)]=...

I was wondering if anyone could help me with this integral. I've heard of contour integration but I'm unsure of how it would be used for this integral.

1. Hi! I am new at this forum, and english is not my native language, so, I hope I can make myself clear. A teacher send us a list of activities, but he did not give us the theory about it (the theoretical class). So, I have read a few things on the internet and I have solved some exercises. I...

Homework Statement \int_{-\infty}^{\infty} |k|^{2\lambda} e^{ikx} dkHomework Equations The Attempt at a Solution As you can guess, this is the inverse Fourier transform of |k|^{2\lambda}. I've tried splitting it from -infinity to 0 and 0 to infinity. I've tried noting that |k| is even, cos is...

We have a wave ψ(x,z,t). At t = 0 we can assume the wave to have the solution (and shape) ψ = Q*exp[-i(kx)] where k = wavenumber, i = complex number The property for a Fourier transform of a time shift (t-τ) is FT[f(t-τ)] = f(ω)*exp[-i(ωτ)] Now, assume ψ(x,z,t) is shifted in time...

Can anybody help in in finding the Fourier transform of f(x) = xe^-x where -1<x<0 and f(x)= 0 otherwise?