Fourier Definition and 1000 Threads

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

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...

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?

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 >[/color] 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...

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...

I am beginer in image processing. Any signal whether it is 1D,2D or any multidimensional signal can be represented using combination of number of sine and cosine waves.Similerly any image can be termed as a sinusoidal function. Fourier series and transform plays vital role in image processing...

Hey, I was wondering, since for a convex lens the Fourier transform of a fields is in their real focus plane. Is it for a concave lens that the Fourier transform of a field is in the virtual focus plane? I can't find any book or paper that talks about how concave lenses work in terms of...

I am engineering student and studying signal processing. The term Fourier transform comes in the discussion several times. There are many transforms like Laplace transform,Z transform,Wavelet transform.But as per my view ,Fourier transform is mostly used compared to others in general. My...

Hi, I have a Fourier problem that i do not know if it is valid to do the calculations like this. The Fourier transform looks like this ## \hat{v}(x,\omega) = \frac{\hat{F}(\omega)}{4(EI)^{\frac{1}{4}}i \omega^{\frac{3}{2}}(\rho A)^{\frac{3}{4}}}\left[ e^{-i\left[\omega^2 \frac{\rho A}{EI}...

Homework Statement Derive the FT for a full-wave rectified sine wave, i.e., |sin(wt)| Homework Equations $$1/(√2π)\int_{a}^{b} |Sin[wt]| {e}^{-i w t}dt$$ The Attempt at a Solution I'm not entirely sure how to start doing this problem. What I tried doing was noticing that both of these...

1. A transversely directed transient force F(t) acts at the free end of a semi-infinite beam. a) Show how displacement, velocity, acceleration and strain at an arbitrary position along the beam can be determined. b) Calculate (MATLAB) the transversal acceleration (or an other quantity) at an...

We know that Fourier Transform F(W) of function f(t) is summation from -infinity to +infinity product of f(t) and exp^{-j w t}Here, what does the exponential term mean?

Hi. I'm familiar with Fourier series but I have some hard times in learning Fourier transform. Why we use it? What's purpose of Fourier transform? Here is one signal and plot of Fourier transform of that signal: What this graph tells us? Thanks in advance.

Hi, I'm working with a Digital Micro-mirror Device type SLM and my goal is to convert my laser from a gaussian to flat-head intensity profile. And then the tricky part is to make the beam oscillate up and down on the camera using just the SLM. Apparently I was to naive to think that moving my...

Homework Statement You have series expansions of the function f(x) = 0 from 0 to .5, and 1 from .5 to 1 : the halfrange cosine series, the half-range sine series, and the Fourier series. For each of these series, find the actual sum of the series at x = 0, and x =1/2, and x =1 Homework...

I'm having trouble understanding a part in my book. second to last paragraph where it says 4.2 must be the Fourier sine series for x^2, how did the author arrive at that? http://i.imgur.com/gLLUYXw.jpg

Homework Statement derive the Fourier sine and cosine transforms of $$f(x) = e^{-cx}$$ by using $$e^{iax}=cos(ax)+isin(ax)$$ and computing the integral $$\int_0 ^{\infty} e^{-cx}e^{iax}dx$$.Homework EquationsThe Attempt at a Solution i'm completely clueless, all i did was evaluate what they...

during these first few steps, where did the constants in front of the integrals come from for a_0,a_n, b_n? http://i.imgur.com/rky0mdf.png (wasn't sure whether to post this as a separate topic or back with the other one)

actually have two questions: here we have a Fourier series.. $$f(t) = \sum c_k e^{2\pi ikt}$$ (c is complex) if we're trying to express a real function via Fourier series, and we do it the following way.. Impose condition: $$\overline{c_k} = c_{-k}$$ $$f(t) = \sum\limits_{k= -n}^n c_k e^{2\pi...

Homework Statement Find the Fourier Coefficients for the triangular wave equation shown in this picture: Homework Equations ##f(t)= a_0 + \sum_{n=1}^\infty a_{n}cos(n{\omega}t) + \sum_{n=1}^\infty b_{n}sin(n{\omega}t)## ##a_0 = \frac{1}{\tau}\int_{-\tau/2}^{\tau/2} f(t) \, dt## ## \omega =...