Fourier transform Definition and 1000 Threads

Find the DTFT of: h[n]=(-1)^{n}\frac{sin(\frac{\pi}{2}n}{sin(\pi n} useful properties: x[n]y[n] --> X[Ω]*Y[Ω] \frac{sin(\frac{\pi}{2}n}{sin(\pi n} --> rect[\frac{2Ω}{\pi} I have no clue how to deal with the (-1)[itex]^{n}[\itex] the DTFT of that doesn't converge. . . any help...

Hi, (To cut a long story short, can I cancel the integrals in Eq. 6 to leave me with Eq. 7?) I am trying to follow the method for modelling the motion of a tethered bead from a couple of papers ("Te Velthuis, A. J. W. et al. (2010) Biophys. J. 99 1292–1302" and "Lansdorp, B. M., & Saleh, O...

At page 285 in Peskin and Schroeder's Introduction to quantum field theory the author defines the integration measure D\phi = \Pi_i d\phi(x_i) where space-time is being discretised into a square lattice of volume L^4. He proceeds by Fourier-transforming \phi(k_n) = \frac{1}{V} \sum_n e^{-i...

Hi, I am learning Fourier transformation by my own. I am reading a book "Fourier Transformation" by R. Bracewell. In chapter 11, in examples of discrete Fourier transforms, it gives for N =2, {1 0} transforms to 1/2{1 1}. I can do this in MATLAB but I can't figure it out how to do it by hand...

is the interference pattern produced by a double slit a one dimensional phase/amplitude Fourier transform? and if you did a reverse Fourier transform on it would you get an image of the two slits?

I've been taught (in the context of Sturm-Liouville problems) that Fourier series can be explained using inner products and the idea of projection onto eigenfunctions in a Hilbert space. In those cases, the eigenvalues are infinite, but discrete. I'm now taking a quantum mechanics course, and...

Homework Statement Hello I'm learning Fourier transforms via the Stanford lecture series on Youtube. In the 6th lecture, the professor claims that the FT of a triangle function is the square of the sinc function. I'm trying to derive this, but I can't get my math to work out. Could someone...

Homework Statement See Attachment Homework Equations The Attempt at a Solution Ok so in a previous question I worked out fd = e-ipd*2*sinc(pa)/√(2∏), also worked out its Fourier transform if that helps. Now I really am stuck on the question, any guidance would be appreciated...

Homework Statement Just wondering if my output seems wrong. The interpolating polynomial looks like it's way off, though I've looked over my code many times and it seems right (?). clc clear all format long x1=[1:1/10:4]; y1=zeros(1,length(x1))...

If I have a signal, sampled at N data points with a time-interval of T, does this restrict the frequency resolution I can obtain in Fourier space? I understand that from the Nyquist-Shannon sampling theorem it follows that all information on the Fourier transform of a T-sampled signal is...

I have a lot of questions, if you know something in one of them or more I will glad if you can write a replay I search after researches or others things that are correlated between optimal control and autonomous vehicles it can be things like how to calculate the shortest way, the rapid way...

Homework Statement How can I figure out the Fourier transform of the following: I'd prefer to use tables if at all possible. 1. d(z)=d_{eff}sign[\cos[2\pi z]/\Lambda]) (note this is one function inside another one.) 2. d(z)=d_{eff}(1/2)(sign[\cos[2\pi z]/\Lambda]+1) 3...

Dear people, I am trying to analyze data from test bench which consists of a magnetically levitated spindle. We have a rotor/spindle which rotates and moves vertically up and down as it rotates. I measure the angle of rotation and the verticle displacement at a steady rate of 10,000 samples...

I need more help understanding Fourier Transforms. I know that they transform a function from the time domain to the frequency domain and vice versa, but the short cuts to solve them just straight up confuse me. http://www.cse.unr.edu/~bebis/CS474/Handouts/FT_Pairs1.pdf This list of relations...

Hi all, I'm reading the following PDF about the DFT: http://www.analog.com/static/imported-files/tech_docs/dsp_book_Ch8.pdf Please see pages 152-153. So the inverse DFT (frequency to space, x[i] = ...) is given on page 152. Then it is claimed that the amplitudes for the space-domain...

Homework Statement Consider a Gaussian pulse exp[-(t/Δt)^2/2]exp(i*w*t), where Δt is its approximate pulse width in time. Use the Fourier transform to find its spectrum. Homework Equations The Fourier transform of a Gaussian is a Gaussian. If a Gaussian is given by f(t) = exp(-t^2/2)...

Hi All, Usually the Fourier transform is defined as the one in the Wiki page here (http://en.wikipedia.org/wiki/Fourier_transform), see the definition. My question is can I define Fourier transform as \intf(x)e^{2\pi ix \varsigma}dx instead, i.e., with the minus sign removed, as the...

Hi. I have been given a plot for 1 Hz, sampled at 0.2 sec. And, 4 Hz and 11 Hz has also been plotted. So, from the plot, I can see that its really hard to distinguish between the signals after digitalization. My question is how do I find the next higher frequency which, when sampled at 0.2 secs...

Homework Statement I'm trying to derive the result on slide 1 of this link: http://www.physics.ucf.edu/~schellin/teaching/phz3113/lec13-3.pdf Unfortunately, I'm not sure how to integrate the Fourier transform when my u(x,t) function is undefined. Could someone help me get the...

Homework Statement I have been given the following: A(r', ω) = μ/4∏*∫ J(r', ω)*exp(-j*k*R)/R dV' And am being asked to find the inverse FT of A(r', ω) Homework Equations Given that k = ω/c and R = |r - r'| The Attempt at a Solution I know what the inverse FT transform is, but...

The DCT of an even function is comprised of just cosine coefficients, correct? I'm playing around in MATLAB and I came up with a simple even function 1.0000 0.7500 0.5000 0.2500 0 0.2500 0.5000 0.7500 1.0000 0.7500 0.5000 0.2500 0 0 0 0...

I know the result: \widehat{H(f)}=i\textrm{sgn}\hspace{1mm}(k)\hat{f} I thought I could use fft, and ifft to compute the transform easily, is there a MATLAB command for sgn? Mat

Homework Statement See figure attached. Homework Equations The Attempt at a Solution See pdf attached for my attempt at the solution. I'm a little confused as to how to draw the phase spectrum for y(t). Would it simply be a line equation of, -\frac{\pi}{6000}f \pm...

Homework Statement Is the Fourier transform of a even/odd function also even/odd ? Homework Equations The Attempt at a Solution So far this result seems to be true. I can't find a confirmation however... Thanks ahead. Daniel.

Homework Statement Hi there! I'm just trying to figure out the Fourier transform of the hyperbolic secant function... I already know the outcome: 4\sum\ ((-1)^n*(1+2n))/(ω^2*(2n+1)^2) But sadly, I cannot figure out how to work round to it! :( maybe one of you could help me... Homework...

Why does a discrete Fourier transform seems to produce two peaks for a single sine wave? It seems to be the case that the spectrum ends halfway through the transform and then reappears as a mirror image; why is that? And what is the use of this mirror image? If I want to recover the frequency...

Homework Statement Find the cosine Fourier transform of the function f(t)=e-at Homework Equations The Attempt at a Solution F(w)=(2/π)0.5∫dt e-atcos(wt) The integral is from 0 to +∞ Using euler's formula I got the result F(w)=(2/π)0.5( eit(w-a)/i(w-a) - e-it(w+a)/i(w+a)...

Trying not to get too confused with this but I'm not clear about switching from coordinate representation to momentum representation and back by changing basis thru the Fourier transform. My concern is: why do we need to change basis? One would naively think that being in a Hilbert space where...

Homework Statement a) Find the Fourier transform of the function f(x) defined as: f(x) = 1-3|x| , |x|<2 and 0 for |x|>2 b) Find the values of the inverse Fourier transform of the function F(k) obtained in a) Homework Equations F(k) = \frac{1}{\sqrt{2π}}\int f(t) eikx dx f(x) =...

I've been trying to figure out why it's standard to use complex discrete Fourier transforms instead of just the real version. It's discussed a bit here. http://dsp.stackexchange.com/questions/1406/real-discrete-fourier-transform As far as I can tell there's a hypothetical efficiency...

In calculating some basic Fourier transform I seem stumble on the proble that I don't know how to take the limit in infinity of an exponentialfunction with imaginary exponent. In the attached example it just seems to give zero but I don't know what asserts this property. I would have thought...

Homework Statement A function f(x) has the following series expansion: ##f(x)=\sum _{n=0}^\infty \frac{c_n x^n}{n!}##. Write down the function ##g(y)=\sum _{n=0}^\infty c_n y^n## under a closed form in function of f(x). Homework Equations Not sure at all. The Attempt at a Solution...

Homework Statement I am looking at finding the Fourier transform of: f(t)=\exp \left[ \frac{-(t-m)^2}{2 \sigma^2}\right] Homework Equations \hat{f}(t)=\frac{1}{\sqrt{2 \pi}} \int_{-\infty}^{\infty} f(t) e^{-i \omega t} dt The Attempt at a Solution I did it a little differently that my...

Here's my problem;Find the Fourier transform \(P(\omega)\) of the function;\[ p(t)=\left\lbrace \begin{array}{ll} e^{-9t} & \text{for } t \ge 0 \\ e^{9t} & \text{for } t \lt 0 \end{array} \right.\]Hence (use one of the shift theorems) find the inverse Fourier transform of; \(...

I was going to post this in the learning material section but i didnt have access to it for some reason. but i guess i can post it here. its homework after all. so i have noticed that there is almost nothing learning material on fourer transform on the web. like how to transform a function to...

Homework Statement For a physics problem I must take the inverse Fourier transform of 2 functions. Namely I must compute the integral ##\frac{1}{\sqrt{2\pi}}\int_{-\infty} ^\infty [A\cos (ckt)+B\sin (ckt)]e^{ikx}dk##.Homework Equations Already given. i is the complex number. t is greater or...

Homework Statement Hi All, I'm just trying to practice graphing signals in frequency domain and I came across a stiuation I wasn't familiar with. If the exp() has a constant*t in it I'm not sure how to graph it, I remember that just cos it like a double sided exp(jwt) but with half the...

Evaluating a "Fourier Transform" Integral Homework Statement Evaluate I = ∫[0,∞] e-ktw2 cos(wx) dw in the following way: Determine ∂I/∂x, then integrate by parts. Homework Equations Possibly? The Attempt at a Solution Since integral limits do not depend on x, the partial with respect...

Hi All, I'm just trying to practice graphing signals in frequency domain and I came across a stiuation I wasn't familiar with. If the exp() has a constant*t in it I'm not sure how to graph it, I remember that just cos it like a double sided exp(jwt) but with half the magnitude. I've attached a...

I have calculated a k-space function to be f(k) = \frac{1}{2k} I want to Fourier transform this to find f(x), I have found many different Fourier transform equations...can I use this one? f(x) = \frac{1}{\sqrt{2π}}\int\frac{1}{2k}e-ikxdk Limits fo integration -Infinity to Infinity...

Homework Statement Find the Fourier Transform of: f(t)=\frac{cos(\alpha t)}{t^2+\beta^2} Homework Equations F(\omega)=\frac{1}{2\pi}\int^{∞}_{-∞}\frac{cos(\alpha t)exp(i \omega t)}{t^2+\beta^2} The Attempt at a Solution I start with: cos(\alpha t)=\frac{exp(i \alpha t)+exp(-i...

Homework Statement Ok I know Fourier transform pair for u(t) is pi*del(w)+1/(j*w) Am I right to say the transform pair of u(t)-u(t-1) is [pi*del(w)+1/(j*w)]-[pi*del(w-1)+1/(j*(w-1)] If not what is it? thanks

Say you have some function that is periodic in a parameter k. The discrete Fourier transform from a sampling may be found in the usual way, giving the frequency spectrum in k. But what if I want to find the frequency spectrum in 1/k ? I'm not really sure what this is called, and so I've had a...

Homework Statement I'm trying to Solve for an impulse response h(t) Given the excitation signal x(t) and the output signal y(t) x(t) = 4rect(t/2) y(t) = 10[(1-e-(t+1))u(t+1) - (1-e-(t-1))u(t-1)] h(t) = ? y(t) = h(t)*x(t) --> '*' meaning convolution! I am unsure how to take the Fourier...

Is there a name for a transformation using the orthonormal base s_k(x)=\lceil \sin kx \rceil,\: c_k(x) = \lceil \cos kx \rceil \quad ? So basically a Fourier transform or Fourier series using periodic rectangles. What are the properties? Is there some kind of convolution theorem?

I am having trouble with this homework problem, I know how to get started but I just don't know how to carry through the completion of the problem: Question: Given the Fourier transform of an aperiodic signal X(ω) = 2*sin(3(ω-2π))/ω-2π (a)find its inverse Fourier transform x(t) using...

"Sketch the form of the Fourier transform" - is this right? Question ~ sketch the "form of the Fourier transform" for the function: f(k) = sin^2(ka/2) / (ka/2)^2So I'm thinking it will look like a cos [or sin] graph (shifted so that its 'above' *f(k)=0*) and that there will be some sort...

Homework Statement Show that the normal coordinates for the equation we derived in Problem Set 4, Problem 2 are given by the discrete Fourier transform of an infinite series and the eigenfrequencies corresponding to each k. http://www.ph.utexas.edu/~asimha/PHY315/Solutions-4.pdf The...

Homework Statement Semi-infnite bar (0 < x < ∞) with unit thermal conductivity is insulated at x = 0, and is constantly heated at x = 1 over such a narrow interval that the heating may be represented by a delta function: ∂U/∂t = ∂2U/∂t2 + δ(x-1) U(x; t) is the temperature. Assume...

Homework Statement S(t) = S(0)e^{-i \pi f_{o}t} e^{-t/T^{*}_{2}}, 0 \leq t < \infty S(t) = 0, t < 0 Show that the spectrum G(f) corresponding to this signal is given by: G(f) = S(0) { \frac{T^{*}_{2}}{ 1 + [2 \pi (f- f_{o} )T^{*}_{2}]^{2}} + \frac{i2 \pi (f- f_{o} )...