Fourier Definition and 1000 Threads

Hello everyone, The question that I have may not be fully relevant to the title, but I thought that could be the best point to start the main question! I'm working on 2-D data which are images. For some reason, I have converted my data to a 1-D vector, and then transformed them to the...

Homework Statement Derive ##\sum_{n=1}^\infty \frac{1}{n^2+b^2} = \frac{\pi}{2b}\coth b\pi - \frac{1}{2b^2}## from either ##e^{b\theta} = \frac{e^{2\pi b}-1}{2\pi} \sum_{-\infty}^\infty \frac{e^{in\theta}}{b-in}## for ##0 < \theta < 2\pi##. or ##e^{b\theta} = \frac{\sinh...

There are many waves and oscillations books out there that also include Fourier analysis but very few give the subject a thorough treatment, they just pass it in a few pages. If anybody has any sources(particularly books) that have Fourier analysis and particularly Fourier Transforms, I would...

With Dirac Comb is defined as follow: $$III(t)=\sum_{n=-\infty}^\infty\delta(t-nT)$$ Fourier Transform from t domain to frequency domain can be obtained by: $$F(f)=\int_{-\infty}^{\infty}f(t)\cdot e^{-i2\pi ft}dt$$ I wonder why directly apply the above equation does not work for the Dirac Comb...

I have the following problem:

i have read many of the answers and explanations about the similarities and differences between laplace and Fourier transform. Laplace can be used to analyze unstable systems. Fourier is a subset of laplace. Some signals have Fourier but laplace is not defined , for instance cosine or sine...

My professor in Classical Electrodynamics is great and all, but sometimes he has trouble understanding what it is that I don't understand. So here I am. Let's say we have the some sort of (monochromatic) radiating system generating a electric field with Fourier amplitude Eω(x) and want to...

Is learning Fourier analysis useful for a high school student? If so, which book should I refer for learning the basics of Fourier analysis? This topic is not in my syllabus. But will it be useful for solving problems? (even if its not, it seems interesting to me). I have learned single variable...

Hi, I have a general function u(x,y,z,t). Then, (1) what would be the space-time Fourier transform of G⊗(∂nu/∂tn) and (2) would the relation G⊗(∂nu/∂tn) = ∂n(G⊗u)/∂tn hold true? Here, note that the symbol ⊗ represents convolution and G is a function of (x,y,z) only (i.e. it does not depend on...

Homework Statement Suppose a horizontally stretched string is heavy enough for the effects of gravity to be significant, so that the wave equation must be replaced by ##u_{tt} = c^2u_{xx} - g## where ##g## is the acceleration due to gravity. The boundary conditions are ##u(0,t) = u(l,t) = 0##...

< Mentor Note -- thread moved to HH from the technical forums, so no HH Template is shown > hi I've got a problem that I've partially worked but don't understand the next part/have made a mistake? f(x)=0 for -π<x<0 and f(x)=x for 0≤x≤π i got a0=π/4 and an=0 and bn=0 if n is even and 2/n if n...

http://t.co/XkVpUrtuAA BTW, how to insert a photo url to show an image here at Physics Forum? http://www.dumpt.com/img/viewer.php?file=yfxl69kwf7oisplu6gzw.jpg

Hi Everyone. I want to know what do you think about this Transfer function: T(\omega) = \frac{e^{i\omega\tau}}{1-\rho e^{i2\omega\tau}} If\tau is Real, this function is "good and pretty"(?), because it has a "nice" representation in time with its inverse transform: a delay plus a series of...

Hi, I'm just curious because I know wifi uses digital FFT to send and receive signals. (I can't really remember why) But when I imagine a signal being sent its like a squiggily wave, so what method does the reciever use to approximate the instantanious values of the signal into a mathematical...

Hi In making Fourier Transform of a function, why is it said that large space (r) corresponds to low wavenumber(k)?

Hey all, I am looking for **calculus**(and not all these books of Advanced Engineerigng Math or etc...) books dealing with Fourier Series ,its expansions , half reange extensions etc... I have found that "Stewart'c calculus" includes a chapter dealing generally with Fourier Series but *not *...

Hi, I'm writting a program in the computer and I've to perform a fast Fourier transform to get the frequency domain information. I've read different website, I've watched some videos, etc and I don't fully understand the whole theory about FFT. I've to say that I don't have a solid mathematics...

A convolution can be expressed in terms of Fourier Transform as thus, ##\mathcal{F}\left\{f \ast g\right\} = \mathcal{F}\left\{f\right\} \cdot \mathcal{F}\left\{g\right\}##. Considering this equation: ##g\left(x, y\right) = h\left(x, y\right) \ast f\left(x, y\right)## Are these steps valid...

Hi all. I have to do Fourer inversion of an equation 7.46 but I don't know how to do that. If anybody has any idea it wolud be very helpfull. Inversion of S(q) is G(r).

I need a good book on the Fourier transform, which I know almost noting about. Some online sources were suggesting Bracewell's "The Fourier Transform & Its Applications." I gave it shot, but it's competely unreadable. On page 1 he throws out an internal expression and says "There, that's the...

The Fourier Transform transforms a function of space into a function of frequency. Considering a function ##f\left(x, y\right)##, the Fourier Transform of such a function is ##\mathcal{F}\left\{f\left(x, y\right)\right\} = F\left(p, q\right)##, where ##p## and ##q## are the spatial frequencies...

It's been quite a few years but I recently watched a video about how every picture can be represented by a number of overlapping constructive and destructive peaks from a Fourier (transform or series? I don't remember which). I remember that Fourier series was for periodic and transform was for...

I was told to do a Fourier transform of function by using a Filon's method. I have found the code but I don't know how to include any function to the subroutine. I would be grateful for any example of how to use this code. SUBROUTINE FILONC ( DT, DOM, NMAX, C, CHAT ) C...

Hello guys. I need an easy explanation regarding Laplace Transform and Fourier Transform. I know it is quite a mathematics question but I need an explanation in which it has something to do with engineering. I already search a bit about them but still cannot find and explanation that easy enough...

Hello, I am trying to find Fourier Bessel Transform (i.e. Hankel transform of order zero) for Yukuwa potential of the form f(r) = - e1*e2*exp(-kappa*r)/(r) (e1, e2 and kappa are constants). I am using the discrete sine transform routine from FFTW ( with dst routine). For this potential...

We know that in the Fourier transform formula ,there are mainly two terms function f(t) and complex exponential term ( function). But I am confused that what should i call Fourier transform formula as a correlation or convolution formula? So can anybody help regarding it?

Homework Statement Use a spreadsheet to determine the F.S. of the data given in Fig 6 See attached for Fig 6 Homework Equations N/A - Use the Fourier Series tool of MS Excel. Tools > Data Analysis > Fourier Series. If you don't have the Data Analysis tool loaded you can load it by going...

(1) For a real function, g(x), the Fourier integral transform is defined by g(x) = \int_{0}^{\infty} A(\omega )cos(2\pi \omega x)d\omega - \int_{0}^{\infty} B(\omega )sin(2\pi \omega x)d\omega where A(\omega ) = 2 \int_{-\infty}^{\infty} g(x)cos(2\pi \omega x)dx and B(\omega ) = 2...

I am working on a project which is based on importance of phase only reconstruction of a signal obtained from fft. Now ,I have detected vehicles from the Video of Traffic on road taken using stationary camera ( Please download the 1.47 MB video for testing MATLAB Code by ( step1) click on the...

We know that Fourier series is used for periodic sinusoidal signals and Fourier transform is used for aperiodic sinusoidal signals. But i want to know that Is there any relation present between Fourier Series and Fourier transform ? Also,Can we derive mathematical formula of Fourier...

Are the results of the Angular Spectrum Method and the Fourier Transform of a Fresnel Diffraction be different, or the same? Given the same distance between the input and output plane, and the same aperture.

Hello all, I'm a third year university physics major. I haven't read much on Fourier analysis however I have had been introduced to it through an oscillations and waves class. My professor was saying that it can be applied to many different areas and is extremely helpful tool to have under your...

Homework Statement given a continuous-time signal g(t) . Its Fourier transform is G(f) ( see definition in picture / "i" is the imaginary number) . It is required to find the Fourier transform of the shifted-time-reversed signal g(a-t) where a is a real constant . That is , find the Fourier...

Hello, I am having a bit of trouble with calculating the Fourier transformation of a harmonic load. I have the function f(t) = A * sin(ωt) in the time-domain. I would like to represent this function in the frequency domain. What would be its amplitude? Thank you

Hi, There is the following function whose Fourier transform I cannot work out despite days of labour, $$f(q) = \frac{e^{i\sqrt{q^2+1}a}}{\sqrt{1+q^2}}.$$ Here ##a## is a nonnegative constant. As usual, the Fourier transform is $$F(x) = \int^{\infty}_{-\infty}dq~e^{iqx}f(q).$$ I tried to use...

Homework Statement I am trying to work out the Fourier coefficient a_{n} for : Mathematics is not my strong point and I would appreciate some help. The answer that wolfram spits out it lovely and neat and I am struggling to get my answer to it. Homework Equations The Attempt at a...

Hello! (Wave) I want to write a version of FastFourierTransform(fft) for the case that $N$ is a power of $3$, seperating the input-vector into $3$ subvectors, solving the problem recursively at them and combining the solutions of the subproblems. I have tried the following: We assume that...

This is a soft question but I think it's a real fact.The Frequency domain has made revolution in the field of Mathematics,Physics,Digital Signal and image Processing etc. Some of concepts which are very difficult to analyse in spatial or time domain can be very easily understood in the frequency...

Homework Statement f'(p) is the Fourier transform of f(x). Show that the Fourier transform of e^(ip0x)f(x) is f'(p - p0). (using f'(p) for transform) Homework Equations f(x) = 1/√(2pi) ∫e^(ipx) f'(p) dp (intergral from -∞ to ∞) f'(p) = 1/√(2pi) ∫e^(-ipx) f(x) dx (also from -∞ to ∞) The...

1. I have the following setting of free space than a lense and again free space i need to solve for the output field as in the figure attached. 3. i used the fresnel transform once and then multiplied the field with the exponential and then convolved all the field. still couldn't make it to the...

When using the Quantum Fourier transform to find the period of the function f(x)\equiv a^x\mod N why is it that the input register is 2n qubits in size and the output register is n qubits?

I am a beginner. The Fourier series, Fourier Transform and it's inverse play very important role in Fourier Analysis and Fourier Synthesis. I have read that Fourier transform is localised in only frequency domain.Also,it contains information about the signal in phase and frequency spectrum...

Hey! :o I want to find the Fourier series of the following function : $$g: [-\pi, \pi]\rightarrow \mathbb{R} \\ g(x)=\left\{\begin{matrix} -\frac{\pi+x}{2} & , -\pi \leq x \leq 0\\ \frac{\pi-x}{2} & , 0<x\leq \pi \end{matrix}\right.$$ I have done the following: $$g \sim...

Homework Statement hello in the college we have Fourier series and i have a problem with the integral limits i add a pdf ( 2 pages only) my question is: how did he get the integral limits from the question the limits are from ##-\pi## to ##-\frac{\pi}{2}## for f(x)=-2 as shown in the first...

I am fond of Fourier series & Fourier transform. In Fourier domain, we can come to know what frequency components are present and the contribution of each component in forming the given signal.But every approach has some advantages and disadvantages.Here, I want to know what are the limitations/...

< Mentor Note -- thread moved to HH from the technical math forums, so no HH Template is shown > Consider a function f(x) = 0, 0 ≤ x < 1 and f(x) = 1, 1 ≤ x < 2 What is the function and how did you find it? Please help it will be used for a Fourier Series project. I can get the Series stuff...

I'm currently working through Nielsen & Chuang's section on the circuit design for implementing the QFT. I'm confused as to why swap gates are used in the model to swap the order of qubits. Heres what I'm looking at http://www.johnboccio.com/research/quantum/notes/QC10th.pdf page 247 figure...

I have computed magnitude and phase spectrum of very famous image of cameraman using fft function in MATLAB.Here,we get magnitude and phase spectrum of the whole image. But I want to find phase values of the neighboring pixels . So if given gray scale image is of dimensions 256*256 and if I...

Homework Statement Homework Equations The Attempt at a Solution http://imgur.com/7TRWjBg I don't really get what it's asking. I don't know how to define a Fourier series when the boundaries for X are between non-multiples of Pi. On top of that, it has one boundary that has 4<x<2Pi. How can...

Hello everyone have a look at this video of Fourier Decomposition of an image.also we know that Fourier series is given in the image as...