What is Transform: Definition and 1000 Discussions
In mathematics, the Laplace transform, named after its inventor Pierre-Simon Laplace (), is an integral transform that converts a function of a real variable
t
{\displaystyle t}
(often time) to a function of a complex variable
s
{\displaystyle s}
(complex frequency). The transform has many applications in science and engineering because it is a tool for solving differential equations. In particular, it transforms linear differential equations into algebraic equations and convolution into multiplication.For suitable functions f, the Laplace transform is the integral
The unilateral laplace transform integrates from 0 to infinity.Then how can i take laplace transform of exp(t)u(-t)?PS:I don't want to flip it and use time scaling property.
Hi,
I have an idea which when tested looks like its clearly flawed. I am hoping someone can tell me where my procedure is flawed, or point me to some other theory that has already done something similar.
The first two are the laplace transform.
The third line is the Fourier Transform.
The...
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...
Hi,
There is the following function whose Fourier transform I cannot work out despite days of labour,
$$f(q) = \frac{e^{i\sqrt{q^2+1}a}}{\sqrt{1+q^2}}.$$ Here ##a## is a nonnegative constant. As usual, the Fourier transform is
$$F(x) = \int^{\infty}_{-\infty}dq~e^{iqx}f(q).$$ I tried to use...
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...
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?
Do two inertial observers in relative motion agree on their relative velocity? Velocity is distance per unit time and they don’t agree on the distance or the elapsed time. If the apparent distance in the prime system is shorter and the elapsed time is longer, then it seems that the apparent...
Homework Statement
Homework Equations
Laplace Trasformations
The Attempt at a Solution
a. done
b. f(t)= t -3*t*u(t-1) + 4*u(t-1) -3*u(t-2) -2*t*(t-2)
c. 1/(s^2) - (3e^-s -2e^-2s)/(s^3) + (4e^-s -3e^-2s)/s
d. 1/(s-1) * (1/(s^2) - (3e^-s -2e^-2s)/(s^3) + (4e^-s -3e^-2s)/s)
These are the...
Homework Statement
f(t)=tcos(4t)Homework Equations
tnf(t)=(-1)n dF(s)/dsn
The Attempt at a Solution
I don't understand why this formula is giving me the oppiste sign of the answer.
If I apply the formula I get
(16-s2)/(s2+16)2
Because n=1 I need to multiply by a negative but this yields...
Hi all.
Sorry about creating this new threat despite existing some others on the same topic.
I have a problem in understanding a very specific step in the mentioned proof.
Let me take the proof given in this link as our guide.
My problem is just at the ending. When it says:
"The region...
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...
Hi everyone,
I am facing some problems in performing clarke-park transform for an induction motor(4 pole stator, squirrel cage IM).
The motor is run with three sine wave inputs, 120 degrees phase shifted with each other.
I am measuring the rotor position from the encoder and using twice of...
Hi!
Here is my task:
Find inverse z transform of $$X(z)=\frac{1}{2-3z}$$, if $$|z|>\frac{2}{3}$$ using definition formula.
I found that $$x(n)$$ is $$\frac{1}{3}(\frac{2}{3})^{n-1}u(n-1)$$ (using other method). But how can I find it using definition formula, $$x(n)=\frac{1}{2\pi j}\oint_{C}^{ }...
Hi!
My task is to find discrete signal x(n), if z transform of that signal is $$X(z)=\frac{5}{(z-2)^{2}}$$. It is known that signal is causal. Here is what I have done. Since signal x(n) is causal, convergence of z transform of that signal will be outside of circle with radius r:
We have in...
< Mentor Note -- thread moved to HH from the technical math forums, so no HH Template is shown >
So this is the problem
Here is the question:
A 32lb weight strecthes a spring 2ft.The weight is released from rest at the equilibrium position. beginning at t=0, a force equal to f(t)= sint acts on...
I am engineering student and studying signal processing. The term Fourier transform comes in the discussion several times. There are many transforms like Laplace transform,Z transform,Wavelet transform.But as per my view ,Fourier transform is mostly used compared to others in general.
My...
Homework Statement
Derive the FT for a full-wave rectified sine wave, i.e., |sin(wt)|
Homework Equations
$$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...
Hello, can you suggest a good book reference to find this:
I have a 3D coordinate system where the axis are:
1) locally tangential to a spiral in the equatorial plane;
2) perpendicular to 1 in the equatorial plane;
3) colatitude.
The direction of axes 1 and 2 changes with position.
I need to...
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?
Homework Statement
f(t) = e^t when 0≤t<1
and 0 when t≥1
Homework Equations
Laplace transformations
The Attempt at a Solution
so the Laplace integral becomesfrom 0 to 1 ∫e^(st^2)dt + 0
how do I integrate this?
I'm having a very hard time understanding how the QFT can be realized using just the Hadamard and controlled rotation gates. Furthermore, I cannot see why swap gates are used to reverse the order of the qubits. I'm embarrassed that don't have much by way of any attempt to show here since I am so...
Homework Statement
How can I take the Inverse Laplace Transform of $F(s) = \frac{d}{ds}\left(\frac{1-e^{5s}}{s}\right)$?
I have tried going with inverse of the derivative and convolution (even tried evaluating the derivative and go from there) but although I can get to some results none of them...
Homework Statement
The Plots bellow show two discrete time signals, in the plots only the initial proportion is shown. Then the signals remain constant and equal to the last value shown. Derive the Z transform of each Signal.
The attempt at a solution
I can get part A, giving an answer of...
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.
Solve by Laplace Transforms.
So I'm stuck on how to find this \mathcal{L}^{-1} $( \frac{\frac{5s}{4} + \frac{13}{4}}{s^2+5s+8} ) $
I'm not sure what t odo. I was thinking I need to use the $\cos(at)$ and $\sin(at)$ formulas but I'm not sure... Any help would be great
Solve by Laplace Transforms.
$y'' + 4y' + 4y = e^t$ $y(0) = 1$, $y'(0) = 0$So I've got
$s^2Y - s + 4sY - 1 + 4Y = \frac{1}{s+1}$
then I got:
$ Y = \frac{s^2+2s+2}{(s+2)(s+2)}$
Now here is where I am getting lost on the partial fraction decomposition..
I've got $s^2+2s+2 = A(s+2) + B$ I...
I was wondering whether this can be done:
Let's say you have transfer function that goes like this:
\frac{Y(s)}{U(s)}= \frac{N(s)}{D(s)}
Now let's say I divide my transfer into two:
\frac{Y(s)}{Z(s)}= N(s)
\frac{Z(s)}{U(s)}= \frac{1}{D(s)}
Can I apply the Laplace Inverse to these two...
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$$.Homework EquationsThe Attempt at a Solution
i'm completely clueless, all i did was evaluate what they...
Hello,
Im not sure if it is the right place to ask it but anyway ...
i got this function:
\begin{equation}
M(t)=\sum\limits_{q=1}^N \frac{v^2}{N+ \frac{1}{2}} \cot^2 \left(\frac{\alpha_q}{2}\right) {\sin^2\left(\sin\left(\frac{\alpha_q}{2}\right)t\right)}
\end{equation}
where:
\begin{equation}...
Homework Statement
$$u_{xx} + u_{yy} = 0 : x < 0, -\infty < y < \infty$$
Homework Equations
We can use Fourier Transform, which is defined over some function ##f(x)## as ##F(f(x)) = 1/ 2\pi \int_{-\infty}^{\infty} f(x) \exp (i \omega x) dx##.
The Attempt at a Solution
Using the Fourier...
Textbook says, Fourier transform expresses a function in time domain as a function in frequency domain. Basically, Fourier transform gives two different expressions in terms of t domain and f domain but they represent the same signal.
It also says Hilbert transform is a different type of...
hi pf!
My book presents a problem and has it boiled down to $$S(u) = -S(f(x)) \exp(- \omega y) / \omega$$ where ##S(u)## is the sine Fourier transform of the function ##u##. However, we cannot directly take the transform back since the singularity at ##\omega = 0##. Thus the book then takes...
Hi.
I`m new here and I need some help with Inverse Laplace Transform: f(t)=5+3t+e^3t g(t)=(t+1)u(t-2) g(t)=(t^2-9t+20)u(t-5) and Laplace Transform: F(s)=1/(s+2)^5 F(s)= 2s^2+10/s(s^2+2s+10) G(S)=2s/s^2+4e^-sso if anywone can please help me:)
Homework Statement
Given x[n] with transform X(ejw), find the Fourier transform in terms of X(ejw).
x1[n]=[0.9ncos(0.6*pi*n)] * x[n-2]
Homework Equations
time shift: x[n-k] -> e-jwkX(ejw)
convolution: x[n] * h[n] -> X(w)H(w)
freq. shift: x[n]ejwcn -> X(ew-wc)
The Attempt at a Solution
I...
Hi, Please I need some help, how can I get the Laplace transform of the integration of a difference equation??
$\int _{ 0 }^{ \infty }{ { e }^{ -st } } \int _{ -\tau }^{ 0 }{ G(\theta )x(t+\theta )d\theta } dt$
Many thanks in advanced.
Hi PF! I was wondering if you could clarify something for me. Specifically, I am solving the heat equation ##u_t = u_{xx}## subject to ##| u(\pm \infty , t ) | < \infty##. Now this implies a solution of sines and cosines times an exponential. Since we have a linear PDE, we may superimpose each...
Homework Statement
I am given f(t) = e^-|t| and I found that F(w) = ##\sqrt{\frac{2}{\pi}}\frac{1}{w^2 + 1}##
The question says to use the nth derivative property of the Fourier transform to find the Fourier transform of sgn(t)f(t), and gives a hint: "take the derivative of e^-|t|"
I also...
I have recorded a micrograph of a 2-D array at a magnification of 43,000x on my DE-20 digital camera, which has a 6.4 μm pixel size and a frame size of 5120 × 3840 pixels. This magnification is correct at the position of the camera. I then compute the Fourier transform of the image. What is the...
I'm trying to solve Laplace equation using Fourier COSINE Transform (I have to use that), but I don't know if I'm doing everything OK (if I'm doing everything OK, the exercise is wrong and I don't think so).
NOTE: U(..) is the Fourier Transform of u(..)
This are the equations (Laplace...
I need to know what's the Residue Theorem for a Laplace Transform. Does anyone know the name or something, so I can search it? I couldn't find anything.
For example, if I have this two equations:
X(s).(s-1) = -Y(s)+5
Y(s).(s-4) = 2.X(s)+7
I know how to solve them using Simple Fractions, but...
Below is my walkthrough of a Fourier transform. My problem is that I want to do all the similar steps for a Fourier transform between position x and the wave vector k. That is working on a solution of the maxwell equations. The maxwell equations has many possible solutions for example:
$$...
Prof Ramamurti Shankar has this Youtube video 'Introduction to Relativity' at
And in it he derives the Lorentz Transforms something like this, at about 58 minutes into it.
|------------------------- t ----------------------| time
|-----ut---------------|---------- x' -------------|...
Homework Statement
Homework EquationsThe Attempt at a Solution
I tried to attempt the question but I am not sure how to start it, at least for part (i).
My biggest question, I think, is how does the multiplication of a random complex number to a Fourier-Transformed signal (V(f)) have an...
Homework Statement
Homework Equations
The Attempt at a Solution
I did Fourier transform directly to the eigenvalue equation and got
Psi(p)=a*Psi(0)/(p^2/2m-E)
But the rest, I don't even know where to start.
Any opinion guys?