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...
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...
%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...
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...
Given a function F(t)
$$ F(t) = \int_{-\infty}^{\infty} C(\omega)cos(\omega t) d \omega + \int_{-\infty}^{\infty} S(\omega)sin(\omega t) d \omega $$
I am looking for a proof of the following:
$$ \int_{-\infty}^{\infty} F^{2}(t) dt= 2\pi\int_{-\infty}^{\infty} (C^{2}(\omega) + S^{2}(\omega)) d...
Well what I did was first use the inverse Fourier transform:
$$u(x,t)=\frac{1}{2\pi }\int_{-\infty }^{\infty }\tilde{u}(\xi ,t)e^{-i\xi x}d\xi$$
I substitute the equation that was given to me by obtaining:
$$u(x,t)=\frac{1}{2\pi }\left \{ \int_{-\infty }^{\infty}\tilde{f}(\xi)cos(c\xi...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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...
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:
$$h(t)=\sum_{l=1}^L \sqrt{g_l} \ \delta(t-\tau_l).$$...
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} +...
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...
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...
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) =...
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...
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...
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...
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...
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...
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...