1. ### I Randomizing phases of harmonics

Suppose I decompose a discrete audio signal in a set of frequency components. Now, if I would add the harmonics I got, I would get the original discrete signal. My question is: if I would randomize the phases of the harmonics first, and then add them, I would get a different signal, but would it...
2. ### Discrete Fourier transform question

Summary:: Discrete Fourier transform exam question Hi there, I'm not really sure how to do this question at all. Any help would be appreciated.
3. ### A Partial differential equation containing the Inverse Laplacian Operator

I am trying to reproduce the results of a thesis that is 22 years old and i'm a bit stuck at solving the differential equations. Let's say you have the following equation $$\frac{\partial{\phi}}{\partial{t}}=f(\phi(r))\frac{{\nabla_x}^2{\nabla_y}^2}{{\nabla}^2}g(\phi(r))$$ where ##\phi,g,f## are...
4. ### Engineering Reconstruct a signal by determining the N Fourier Coefficients

%My code: %Type of signal: square T = 40; %Period of the signal [s] F=1/T; % fr D = 23; % length of signal(duration) dt=(D/T)*100; N = 50; %Number of coefficients w0 = 2*pi/T; %signal pulse t1= 0:0.002:T; % original signal sampling x1 = square((2*pi*F)*(t1),dt);%initial square signal...
5. ### I Separation of variables - Getting the Fourier coefficients

Hey there! I am current taking an introductory course on PDE's, and our professor hasn't really emphasized last part of solutions from separation of variables. Now its not strictly going to be on the exam, however I remember doing this with ease a few years back, but for some reason now I...

8. ### A Finding a specific amplitude-frequency in the time domain

Hello, I have a signal and got the FFT result of that. I have shown them both below along with the MATLAB code. May I ask if there is any method to find the time zone(s) in the signal that a specific frequency has(have) happened? The reason I'm asking this is that I want to specify the time...
9. ### I Fourier's Trick and calculation of Cn

I understand that the solutions to the time-independent Schrodinger equation are complete, so a linear combination of the wavefunctions can describe any function (i.e. ##f(x) = \sum_{n = 1}^{\infty}c_n\psi_n(x) = \sqrt{\frac{2}{a}} \sum_{n=1}^{\infty} c_n\sin\left(\frac{n\pi}{a}x\right)## for...
10. ### Heat loss in a conductor based on Fourier's law

Homework Statement Find the admissible current density Jadm for a wire that has no insulation and also for a wire that has two layers of insulation and compare it to Jadm for the case when the wire has only one layer of insulation. 2. The attempt at a solution and equations In the image...
11. ### Extending function to determine Fourier series

In the following question I need to find the Fourier cosine series of the triangular wave formed by extending the function f(x) as a periodic function of period 2 $$f(x) = \begin{cases} 1+x,& -1\leq x \leq 0\\ 1-x, & 0\leq x \leq 1\\\end{cases}$$ I just have a few questions then I will be able...
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### E&M separation of variables and Fourier

Homework Statement Boundary conditions are i) V=0 when y=0 ii) V=0 when y=a iii) V=V0(y) when x=0 iv) V=0 when x app infinity. I understand and follow this problem (separating vars and eliminated constants) until the potential is found to be V(x,y) = Ce^(-kx)*sin(ky) Condition ii...
13. ### A Convolution operator spectrum

Hi everyone, I have some knowledge of Hilbert spaces and Functional Analysis and I have the following question. I ofter have read that "Fourier transform diagonalize the convolution operator". So, we can say that for LTI systems (that can always be described with a convolution and "live" in...
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### Solving the heat equation using FFCT (Finite Fourier Cosine Trans)

Homework Statement Solve the following heat Eq. using FFCT: A metal bar of length L is at constant temperature of Uo, at t=0 the end x=L is suddenly given the constant temperature U1, and the end x=0 is insulated. Assuming that the surface of the bar is insulated, find the temperature at any...
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### Fourier Transform

Homework Statement Hello everyone, am trying to solve this Fourier Trans. problem, here is the original solution >> https://i.imgur.com/eJJ5FLF.png Q/ How did he come up with this result and where is my mistake? Homework Equations All equation are in the above attached picture The Attempt at...
16. ### I Supressed harmonics with certain initial conditions

I'm currently reading class notes from an introductory waves course, written by the professor himself. I'm stuck in the Fourier analysis part, because he gives the formulas for the nth mode amplitude of a standing wave with fixed ends and then states some properties which I can't really make...
17. ### Matching Discrete Fourier Transform (DFT) Pairs

Homework Statement [/B] I am trying to match each of the following 28-point discrete-time signals with its DFT: Set #1: Set #2: Homework Equations The Attempt at a Solution Set #1 We have already established (here) that: ##Signal 1 \leftrightarrow DFT3## ##Signal 4 \leftrightarrow...
18. ### Find Fourier coefficients - M. Chester text

Homework Statement I am self studying an introductory quantum physics text by Marvin Chester Primer of Quantum Mechanics. I am stumped at a problem (1.10) on page 11. We are given f(x) = \sqrt{ \frac{8}{3L} } cos^2 \left ( \frac {\pi}{L} x \right ) and asked to find its Fourier...
19. ### Power signal calculation using Parseval's Theorem

Homework Statement Hi guys, I have the following transmitted power signal: $$x(t)=\alpha_m \ cos[2\pi(f_c+f_m)t+\phi_m],$$ where: ##\alpha_m=constant, \ \ f_c,f_m: frequencies, \ \ \theta_m: initial \ phase.## The multipath channel is: $$h(t)=\sum_{l=1}^L \sqrt{g_l} \ \delta(t-\tau_l).$$...
20. ### A Fourier Transforming a HgTe 2D Hamiltonian

Hi! I am currently trying to derive the Fourier transform of a 2D HgTe Hamiltonian, with k_x PBC and vanishing boundary conditions in the y direction at 0 and L. Here is the Hamiltonian: H = \sum_{k}\tilde{c_k}^{\dagger}[A\sin{k_x}\sigma_x + A\sin{k_y}\sigma_y + (M-4B+2B[\cos{k_x} +...
21. ### Integral of absolute value of a Fourier transform

Homework Statement Hi guys, I am going to calculate the following integral: $$\int_0^{f_c+f_m} |Y(f)|^2\, df$$ where: Y(f)=\frac{\pi}{2} \alpha_m \sum_{l=1}^{L} \sqrt{g_l}\left [ e^{-j(\omega \tau_l - \theta_m)} \delta(\omega - \omega_0) + e^{-j(\omega \tau_l + \theta_m)} \delta(\omega +...
22. ### I Calculating Magnetic Field Strength from FFT

Hello All, Briefly on the exposition; I'm an undergraduate assistant to a professor. We contribute to the Muon g-2 experiment in Fermilab, designing and optimizing the magnetic-measurement equipment. As you might imagine I utilize the Fourier Transform often to analyze data. The data I'm...
23. ### Finding Fourier Coefficient

Homework Statement [/B] I am looking for help with part (d) of this question 2. Homework Equations The Attempt at a Solution I have attempted going through the integral taking L = 4 and t0 = -2. I was able to solve for a0 but I keep having the integrate by parts on this one. I've tried...
24. ### Fourier Series Coefficient Symmetries

Homework Statement Let ## f(x) = \frac{a_0}{2} + \sum_{n=1}^{\infty} (a_n \cos nx + b_n \sin nx) ## What can be said about the coefficients ##a_n## and ##b_n## in the following cases? a) f(x) = f(-x) b) f(x) = - f(-x) c) f(x) = f(π/2+x) d) f(x) = f(π/2-x) e) f(x) = f(2x) f) f(x) = f(-x) =...
25. ### Fourier/heat problem involving hyperbolic sine

Homework Statement A rectangular box measuring a x b x c has all its walls at temperature T1 except for the one at z=c which is held at temperature T2. When the box comes to equilibrium, the temperature function T(x,y,z) satisfies ∂T/∂t =D∇2T with the time derivative on the left equal to zero...
26. ### I Calculating Magnetic Field from FFT Amplitude

So a little bit of background: I work in an undergraduate lab at UMass Amherst and am currently building/optimizing a faraday magnetometer for use in the Muon g-2 experiment at Fermilab. The magnetometer works as follows. A laser is shone through a crystal with a particular Verdet Constant at...
27. ### Fourier Series/Wave Problem

Homework Statement A violin string is plucked to the shape of a triangle with initial displacement: y(x,0) = { 0.04x if 0 < x < L/4 (0.04/3)(L-x) if L/4 < x < L Find the displacement of the string at later times. Plot your result up to the n = 10...
28. ### Arguments of the FT and DTFT

Could someone explain the intuition behind the variables of the FT and DTFT? Do I understand it correctly ? For FT being X(f), I understand that f is a possible argument the frequency, as in number of cycles per second. FT can be alternatively parameterized by \omega = 2 \pi f which...
29. ### I Understanding Fourier Transforms

Hello all, First time poster here so please excuse any mistakes as I'm unfamiliar with the conventions of this forum. Also before I get started I'd like to say I wasn't sure exactly where a question like this would go; I debated in the Math Programs and Latex section but figured general physics...
30. ### Domain of a discrete fourier transform

Homework Statement The (computing) task at hand is to take a function f(x) defined at 2N discrete points, and use the Discrete Fourier Transform (DFT) to produce F(u), a plot of the amplitudes of the frequencies required to produce f(x). I have an array for each function holding the value of...