Fourier analysis Definition and 143 Threads

Homework Statement I am trying to construct a Mathematica notebook that will be able to import sound in the form of a .wmv file and then create the frequency spectrum for a given time interval. Homework Equations I managed to complete this part, though I am trying to figure out: a)...

a question on orthogonality relating to Fourier analysis and also solutions of PDEs by separation of variables. I've used the fact that the following expression (I chose sine, also cosine works): \int_{0}^{2\pi}\sin mx\sin nxdx equals 0 unless m=n in which case it equals pi in...

Hello guys. thanks for reading my thread first. I have been studied classical mechanics and quantum mechanics a little and after that, I got a kind of feeling "I have to study Fourier analysis(FA) again". So I have been studying FA again. Here're my question. 1. From my viewpoint...

Can someone provide me a link that explains and provides a proof for the following principles: 1. Fermat's Principle that light always takes the path that minimizes the time taken 2. Solution to a Fourier Series and why all periodic motion can be represented as an infinite sum of sines and...

Homework Statement The signal y(t) is generated by convolving a band limited signal x1(t) with another band limited signal x2(t) that is y(t)=x1(t)*x2(t) where: --> X1(jω)=0 for|ω| > 1000Π --> X2(jω)=0 for|ω| >2000Π Impulse train sampling is performed on y(t) to obtain: --> yp(t)=...

Dear friends, I generated a time series graph showing some modeled versus measured data (precipitation data)...The results show that the modeled data are sharper than the mesured data (more rounded on top)...Based on that, how can I explain the frequency content changes based on Fourier...

Homework Statement Fourie analysis for a boost converter Where d = duty cycle, A = amplitude and t = time Homework Equations Fx = (2At/d) for 0<t<d/2, -A+(2A/(1-d))*(1-t-d/2) for d/2<t<(1-d/2); (2A/d)*(t-1) for 1-d/2 <t<1. Where d = duty cycle, A = amplitude and t = time The...

Hello everyone(my first post here), I hope I have posted in the right section... Homework Statement Given x[n] is a discrete stable(absolutely summable) sequence and its continuous Fourier transform X(e^{j\omega}) having the following properties: x[n]=0, \ \ \ \forall n<1 and...

So I'm supposed to do this but is it just me or is it too hard to do this analytically? (I put it into wolfram online integrator and he couldn't do it) I don't need it very accurate so are there any approximations to this distribution that I could use to make it easier? Anyone have any ideas of...

Homework Statement let S(R) be the schwartz space, M(R) be the set of moderately decreasing functions, F be the Fourier transform Suppose F:S(R)->S(R) is an isometry, ie is satisfies ||F(g)|| = ||g|| for every g in S(R). Show that there exists a unique extension G: M(R)->M(R) which is an...

I was wondering if anyone has any recommendations for a Fourier Analysis textbook. I have Stein & Shakarchi's Fourier Analysis textbook, but ideally I'd like to have one that takes advantage of some of the analytic machinery that I know that Stein & Shakarchi doesn't assume. I have a basic...

Hi, I am starting in a Ph.D. program in math next fall and the prerequisites for the first-year graduate course sequences included basics of Fourier analysis. The only thing I know about it is that you calculate a projection of a function on a certain infinite dimensional subspace, so I do...

I have a question that I just don't know how to go about. " Let Fn = x/(1+(n^2)(x^2)) where n=1,2,3,... show that Fn converges uniformly on (-infinity,infinity)" To be honest, I don't even know where to start. Is this a series? How would I solve this. Would the Abel's test apply?

Hallo all, i have a problem with Fourier analysis and i really hope yoou can help me in this forum. i have been trying to find the reason for my problem since many weeks but i could not. Well, i have this Equation:s(t) = (1/(4*(Pi*t)^(3/2))) * Exp[-3)/(4*t)] and i need to find the...

Homework Statement I need to find the Fourier coefficients for a function f(t)=1 projected onto trigonometric polynomials of infinite order Homework Equations Equation finding the first coefficient, the constant term: The Attempt at a Solution So I feel quite stupid because this...

I having a hard time understanding an aspect of the definition of the convolution of two functions. Here is the lead up to its definition... It goes on to discuss what the observed distribution h(z) will be if we try to measure f(x) with an apparatus with resolution function g(y). And tries...

Dear all I have recently taken up the study of Fourier analysis. My background knowledge is limited - some basic notions of analysis, including the Riemann integral, as well as uniform and pointwise convergence of series of functions. These are not exactly homework problems, but questions...

I'm an Engineering Physics Major senior and I'm going to get my Masters in Mechanical Engineering. I have an internship in the Polymer and Coatings Department Analyzing Data. I am mostly going to be doing Fast Fourier Transforms and studying the data. The problem is I don't really know...

Hello all, I'm looking for a good textbook, tutorial or anything like that about Fourier analysis: the discrete series and the Transform (very important - for a project about waves). I don't know a lot about Fourier analysis, so this textbook should start quite from the beginning. What I do...

Hi all. I am learning a numerical method that involves Fourier transform. As far as I know, I think Fourier transform is tool to find the frequency spectrum of a signal. And the usual form shall be "Integrate from negtive infinity to positive infinity, f(x)*exp(i*w*x)dx" However, when i...

is Fourier analysis in qft just used for going from a position wavefunction to a wavefunction described by the wave vector (k)? also why is the integral divided by [2(pi)]^n where n is the number of dimensions and how do you know when to divide the integral by the 2(pi) factor or not?

I have an infinite well from -a to with a particle in its ground. The initial wavefunction is then \psi(x) = u_1^+(x;a) = cos(\pi x/ 2a)/\sqrt{a} for |x| < a. In order to get the wavefunction for this particle when box that is instantaneously expanded to [-b,b] should I apply Fourier...

hey does anyone know if studying Fourier analysis is going to aid in physics, particularly in string theory or quantum physics?

hi Im doing a project about chaos theory. Over the past few weeks I've built a Lorenzian waterwheel (its a waterwheel with buckets with holes in them, it shows chaotic behaviour.) One of the aims of the experiment was to try and plot the Lorenz attractor. The lorenz attractor is a strange...

it's a curiosity more than a HOmework, given the integral: \int_{-\infty}^{\infty}dx e^{if(x)+iwx}=g(w) Where g(w) can be viewed as the Fourier transform of exp(if(x)) then my question is if we can prove g(w) satisfies the ODE: -if'(x)\frac{\partial g(w)}{\partial w}+wg(w)=0 for...

I'm just taking Calculus 4 this semester, where part of it is also Fourier analysis. When I was browsing a little bit about the subject I found out that there are several different approaches and so I'm a bit confused now. So this is how I understand it, correct me if I'm wrong: There...

Does anyone know of any good texts that cover Discrete Fourier Analysis and the Fast Fourier Transform? *I don't know if this belongs here in the HW help or in General Math section.

I am trying to compute the DTFT of x[n]=n(.5)^n u[n]. This is my work so far. Is this correct?

Can anyone help me devise some kind of physics related question (ie. How does resistance varry with area?) involving light or sound where the frequency spectum varries when Fourier Analysis is performed? Would "How does the frequency spectrum of a light bulb varry with the voltage across it."...

From what I understand, I can use Fourier Analysis to represent a periodic signal using a sum of sine waves. However, isn't this just a mathematical tool? Can I take any non-monochromatic light source and use Fourier Analysis to break it into a sum of the physically meaningfuly frequencies it's...

I'm supposed to do an "investigation into a physics-related question." for my senior year project. I want to do something realted to Fourier Analysis but I need some sort of experiment. Any ideas? How hard would a computer model be? Also, would this topic fall more under math?

Can anyone recommend an application for PC that can take an audio recording, perform a Fourier transform, and return the audio recordings' frequency spectrum AND phase information? I can find plenty of programs that return the frequency spectrum, but I've had no luck finding one that...

I have a chance to do an Independent Study in place of a regular class (senior, high school), and with my physics teacher as an advisor I've thought of the possibility of doing some work with Fourier Analysis. My problem is I don't know at what level this is normally taught at and what...

I'm puzzled and don't know where to begin with this question; it goes like "Consider the function f:R²-->R defined by f(x,y) = \sum_{n=1}^{\infty}\frac{(-1)^n}{n^2}sin(nx)sin(ny) Show that f is continuous." Any hint? .

This seemingly not-so-harsh math problem has me stumped. I tried solving it every free minute I had this weekend but no trails or any combination of them led me anywhere happy. The little ba$tard goes as follow: "Consider f: [-\pi,\pi)\rightarrow \mathbb{R} a function (n-1) times...

Ok, this might seem like either a really idiotic question or a really profound one. Consider a probability distribution. I'm picturing a normal distribution, is it meaningful to be able to build up a final probability distribution from a set of narrower probability distributions? Ok...

The signal is from a voltage supply. I see lots of pages on the internet about this, such as this one, which shows what the magnitude spectrum looks like for a square wave with an arbitrary number of co-efficients. But how would I actually create that graph myself?

1) Why can't f(x) = 1, -&inf; < x < &inf; be represented as a Fourier integral? Is it because it must be defined on a finite interval? 2) Could someone tell me how you find the embedded harmonics in a given periodic function using Fourier series and integrals? Either a quick demonstration or...

I really need help with this exercise (it's from a course in basic Fourier analysis). It consists of two parts: (i) Let s_0 = 1/2 and s_n = 1/2 + \sum_{j=1}^{n}\cos(jx) for n \geq 1 . By writing s_n = \left(\sum_{j=-n}^{n}e^{ijx}\right)/2 and summing geometric series show that...

Myself and a user on another board have come to the following hurdle we can't overcome: Mathematically we represent an arbiarty matter wave as a superposition of plane waves; using the theory of Fourier analysis. We can write an arbitary wavepacked as a Fourier integral of the form: $\psi...

From the beginning of quantum mechanics the main tool for mathematical analysis was Fourier anaysis. (Heisenberg intoduced his famous matrices using Fourier analysis). Fourier analysis has a non-local character-that the basis functions extend infinitely in space and time. What would be the...

Does it make sense to Fourier-analyse pi(n) for finding patterns toward a comprehensive prime-predictive formula?

Okay, if I want to do a Fourier Analysis of a wavefunction, I can use the following transform pairs for real space and momentum space. &Psi;(x) = (2&pi; hbar)^(-1/2) * &int; dp &Phi;(p) exp(ipx/hbar) &Phi;(p) = (2&pi; hbar)^(-1/2) * &int; dx &Psi;(x) exp(-ipx/hbar) So, what I want to...