Homework Statement
I've been stuck on this for a while:
Find the Fourier transform of f(t)=sin(\omega0t+\phi)
Homework Equations
I know that I have to use F(ω)=\intf(x)e^-iωt dt (between - and + infinity) to solve this
The Attempt at a Solution
So far I have...
I really need your help - i can't work out how to do a FFT in excel. The main problem is I don't have a constant sampling rate - I recorded the time and then the corresponding magnitude of the wave. I have followed everything oneline but I can't seem to get anything to work as I can't fill the...
Homework Statement
Any wavepacket can be obtained by the superposition of an infinite number of plane waves using the so-called Fourier integral or Fourier transform
f(x,t) = \frac{1}{\sqrt{2\pi}} _{-\infty}\int^\infty A(k)e^{i(kx-\omega t)} dk
Find at t=0 the representation of the...
Show G(k)=\sqrt{2π}g1(k)g2(k)
Given that G(k) is the Fourier transform of F(x), g1(k) is Fourier trans of f1(x), g2(k) is Fourier trans of f2(X) and
F(x)=^{+∞}_{-∞}∫dyf1(y)f2(x-y)
SO FAR
G(k)=1/\sqrt{2π}^{+∞}_{-∞}∫F(x)e-ikxdx <-def'n of Fourier transform...
Hi, I am taking a random process class and I came across a problem that has stumped me. I believe I know the end result but I would like to know how it is solved. I have been out of college for a while and I am a little rusty with integration.
Homework Statement
What I need is to find out...
how to get the Fourier transform of (1+at^2)^-n ? n is a natural number such that (n>1) and a is any positive number.
i.e. ∫((1+at^2)^-n)*exp(-jωt)dt; limits of integration goes from -∞ to ∞
Homework Statement
Find the Fourier transform of x(t) = e-t sin(t), t >=0.
We're barely 3 weeks into my signals course, and my professor has already introduced the Fourier transform. I barely understand what it means, but I just want to get through this problem set.Homework Equations
I...
I want to use Matlab and Fourier transforms to solve linear systems and am attempting to implement a very simple linear system (with the idea of implimenting a much more complex one later) that I can't seem to get working. The system will take the derivative with respect to time of the input as...
Hi all, I have a seemingly simple problem which is I'd like to efficiently evaluate the following sums:
Y_k = \sum_{j=0}^{n-1} c_j e^{\frac{i j k \alpha}{n}}
for k=0...n-1. Now if \alpha = 2\pi, then this reduces to a standard DFT and I can use a standard FFT library to compute the...
This is for an assignment, (not sure if its in the right section) but anyway I'm considering the system response to H(w) = 10/(jw + 10)
when the input is x(t) = 2 + 2*cos(50*t + pi/2)
so I know that Y(w) = X(w).H(w) but I'm not sure what to do about the '2 + ' in the input.
I know that...
Homework Statement
The argument of the kernel of the Fourier transform has a different sign for the forward and inverse transform. For a general function, show how the original function isn’t recovered upon inverse transformation if the sign of the argument is the same for both the forward and...
Since I lack the understand of real world applications of Fourier Transform in the real world I decided to buy a signals and systems book (Lathi) do some Fourier Transform problems and them do the same problem in Matlab.
The question in the book wants me to find the Fourier Transform of...
Homework Statement
Determine Fourier Transform of
f(t) = cos^2 ω_p t ... for |t|<T
also, for |t|>T, f(x) = 0, although i don't think you need to do anything with that.
The Attempt at a Solution
okay so:
f(t) = cos^2 ω_p t ... for |t|<T
becomes
f(t) =...
Homework Statement
I am using the time differentiation property to find the Fourier transform of the following function:
Homework Equations
f(t)=2r(t)-2r(t-1)-2u(t-2)
The Attempt at a Solution
f'(t)=2u(t)-2u(t-1)-2δ(t-2)
f''(t)=2δ(t)-2δ(t-1)-??
Can somebody explain what the...
hi
I know the Fourier transform of a lorentzian function is a lorentzian but i was wondering if the Fourier transform of the second derivation of a lorentzian function is also a second derivative of a lorentzian function
Thanks
Hi all,
I've been trying to solve the following
I = \int_{-\infty}^{\infty}\int_{-\infty}^{\infty} \frac{x}{(x^2+y^2+d^2)^{\frac{5}{2}}} e^{-i(kx+\ell y)} \ dx \ dy
where d,k,\ell are constants. I haven't been able to put this into a tractable analytic form and I figured I'd consult all...
Hey Physics Forums,
Grading an assignment, the current topic is continuous Fourier Transforms. They're trying to prove the convenient property:
\mathcal{F} \left[ \frac{d^n}{dx^n} f(x) \right] = (i \omega)^n \mathcal{F} \left[ f(x) \right]
So there's a simple way to get it:
Let f(x) be...
Hi,
I am having a little trouble with the physical meaning of a Fourier transform. I will try to pose a concrete example. Mathematically, the Fourier transform of an exponential decay results in a Lorentzian function.
Let's say I have a population that decays exponentially with time. Now, if...
Hi guys~
I have got a few things about some Fourier transform Q/A that i wanted to check...so here you go:
1) Find the Fourier sine and cosine transform of f(x)=x 0<x<3
ok, for the sine, i get -9/n∏ but i get zero for cosine part, is it wrong?
and the second one:
find the Fourier transform...
I originally asked this in the Calculus & Analysis forum. But perhaps this is better suited as a question in Abstract algebra.
For the set of all Dirac delta functions that have a difference for an argument, we have the property that:
\int_{ - \infty }^\infty {{\rm{\delta (x -...
Hi there,
I have a little problem in wave optics: I have a wave function \psi_{ap} that depends on some geometric parameters, but that has no units itself (as one would expect). But unfortunately when I calculate the Fourier transform of this wave function the Fourier transform has a unit...
Hi
I'm working on a project which takes up ECG signals and tries to evaluate the condition of the patient.
For one particular disease (ventricular tachycardia) the ECG looks close to a sine wave. Hence, I find the predominant frequency in the signal. I shift the original signal now by half...
If you take the absolute value of the FFT output, does that give you the amplitude?
I am asking because I have seen example where that is taken as the amplitude, and examples were the absolute value is multiplied by either SQRT2 or by 2 to get the magnitude.
So my question is what is...
Multi-Variable / Dimension Fourier Decomposition
Say we have f(x, y). We can Fourier decompose it in terms of f1(y, v) and e^{\ x\ v}, f2(x, u) and e^{\ u\ y}, or both variables simultaneously f3(u, v) and e^{\ x\ v\ +\ u\ y}. Similarly for any greater number of variables or dimensions. Now, is...
Hi,
I know this topic is more suited for Computing & Technology, but it has even more to do with general questions about Fourier transform capabilities. I have a question about sample restoration in Discrete Fourier Transform. Suppose we have a signal with the stack of frequencies from 1 Hz...
Homework Statement
The Attempt at a Solution
I don't understand this step. It's got to be some sort of identity that I missed. I also don't understand why the limits of integration change.
Fourier Transform help! (bit urgent)
Hi there,
I'm having a recurring problem with my Fourier transforms that I have tried really hard to figure out but I feel like I'm missing something important. It keeps popping up in my communications and signal processing papers.
I keep getting FTs...
I understand that if you have a system that is linear and time invariant, that you can perform a Fourier transform on it. But that doesn't mean you need to Fourier transform it. Or does it? Is a linear, time invariant system equivalent to or in some way implies a Fourier transform? Or is the...
Homework Statement
F{f(t)} is the Fourier transform of f(t) and L{f(t)} is the Laplace transform of f(t)
why F{f(t)} = L{f(t)} where s = jw in L{f(t)}
The Attempt at a Solution
I suppose the definition of F{f(t)} is
∫[f(t)e^-jwt]dt
where the lower integral limit is -∞...
Just began a serious study of the Fourier transform with a couple of books. One of them defines the Fourier transform on \mathbb R as
\hat f(\xi) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^\infty f(x) e^{-i\xi x}dx.
Another defines it as
\hat f(\xi) = \int_{-\infty}^\infty f(x)...
I'm trying to evaluate the following intergral using complex function theory:
\begin{equation}
\int_{-\infty}^{\infty}\int_{-\infty}^{\infty}\frac{e^{i(ap+aq+b\sqrt{k^2-p^2-q^2})}}{\sqrt{k^2-p^2-q^2}}dpdq
\end{equation}I though that it is possible if i can calculate:
\begin{equation}...
I guess this is programming and physics all combined into one but hopefully I can get some help anyway.
I am doing some signal analysis of real-time streaming sensor data. I would like to do a DFFT on the data in real time as it streams in. So far pretty easy, however, there are a number of...
Hi I am trying to analytically calculate the Fourier transform attached.
I am getting really stuck with the integral, can anyone help?
I've attached how far I've got with it, any help much appreciated!
Kind Regards,
Mike
Hi everyone,
I'm trying to solve an exercise in which I need to find x(t) considering that X(ω) = cos(4ω). So, I need to find the Inverse Fourier Transform of cos(4ω), but I don't have the inverse Fourier transform table.
So, I thought about applying the duality property. If x(t) <-->...
What is the Fourier transform of $f'(ax)$, where a>0 is a constant? Firstly, I reasoned that (lets say $F[f]$ is the Fourier transform of f) $F[f('x)]=\frac{1}{a}F[f](\frac{k}{a})$ by scaling theorem, then using the derivative rule we get $F[f'(ax)]=\frac{ik}{a}F[f(x)](\frac{k}{a})$. But when I...
Ohno Potential is modeled by
v(r)=\frac{U}{\alpha ^{2}r^{2}+1}. U and \alpha are constants.
I try to Fourier transform it
V(q)=\int V(r) e^{iqr\cos \theta}r^{2} \sin \theta d \phi d \theta dr
It gives
V(q) = 2 \pi U \int \frac {r \sin qr}{\sqrt{\alpha ^{2} r^{2}+1}} dr
The...
Homework Statement
I can't figure out what the limits of integration should be;
if a transfer function is given as follows:
h(ω)=1 if 1<|ω|<2, 0 otherwise
1) find the impulse response
2) if the input is white noise of intensity σ² find the variance of the output signal
3)state...
Homework Statement
a) Find the normalization constant N for the Gaussian wave packet \psi (x) = N e^{\frac{-(x-x_{0})^{2}}{2K^{2}}}. b) Find the Fourier Transform and verify it is normalized.
2. The attempt at a solution
a) I think I've got
\psi (x) = N e^{\frac{-(x-x_{0})^{2}}{2K^{2}}}
\int...
Hi everyone, I have a question on the discrete Fourier transform. I already know its a change of basis operator on C^N between the usual orthonormal basis and the "Fourier" basis, which are vectors consisting of powers of the N roots of unity.
But if i recall correctly from complex...
I'm trying to find \frac{1}{2\pi}\int \limits_{-\infty}^{\infty}e^{-itx}\frac{1}{a^2+x^2}\mathrm{d}x where 'a' is a constant.
First I noticed that there is \frac {\partial \arctan x}{\partial x} in this and using a substitute got \int \limits_0^{\pi / 2}\cos( t \tan x )\mathrm{d}x with some...
Homework Statement
f(t)=t*e^(-2t^2)
Find the Fourier Transform F(w) of f(t).
It is given that when f(t)=e^[(-at^2)/2] F(w)=√(2*pi/a)*e^[(-w^2)/2a]
Homework Equations
The Attempt at a Solution
The transform of e^(-2t^2) is easily obtained from the given information, and I got...
Hello Everyone,
Actually my question is related to Window Fourier transform (WFT). I have studied that with the help of WFT we can easily determine the phase of the image. Like by multiplying the window to only a specific part of the input and considering the outside part of the window equals...
Homework Statement
Just something I am working through and am a bit stuck on.
Homework Equations
I have taken the Fourier transform of an RC circuit which gives me :
Y(ω)=((X(ω))/(1+iωτ))
If i take the voltage across the circuit as white noise then i get:
Y(ω)=σ^²/2π/(1+iωτ))
How...
\geqHomework Statement
Find the Fourier Transform of
y = exp(^{}-at)sin(\omega_{}0t) for t ≥ 0
and = 0 for t < 0
Find the amplitudes C(\omega, S(\omega), and energy spectrum \Phi' for \omega > 0 if the term that peaks at negative frequency can be disregarded for pos frequency...
I haven't had differential equations yet, so I am struggling in your math methods class. I understand what a Fourier Transform is, but I'm having trouble with this particular problem.
Homework Statement
Here's a screenshot. Better than I can write it.
http://i.imgur.com/PQ6tB.png
The...
I'm confused about the DFT of the data, fn = cos(3\pin/N) for n=0,1,...,N. It is definitely an even function, and I read that the Fourier coefficients of an even function is real. But when I take the FFT of this in Matlab I get complex numbers, not real numbers. What am I missing?
Thanks ...
Hello all,
I want to extract the period out of a complex discrete signal.
Currently I have the Matlabscript of the attachement.
However, the values I get out of this script are not correct. There is some kind of systematic bias in it.
I think it has something to do with index *...