0
votes
0answers
26 views

Fourier Transform, Laplace Transform, but what about…

I have a question regarding the fourier and laplace transform. First, the Fourier transform essentially takes a function, divides it by a frequency (imaginary exponential), and then sees how much of ...
1
vote
1answer
80 views

Laplace Transform and Fourier Transform of a function

I have this transfer function: $$ h(t)= -\frac{1}{16}te^{-2t} $$ and the Laplace Transform is: $$ H(s) = \frac{-\frac{1}{16}}{(s+2)^{2}} $$ I know that to find the Fourier Transform, I would ...
1
vote
0answers
66 views

Calculating convolutions of probability density functions

I have a PDE: $$\frac{\partial N (x,u)}{\partial x}=\int _0^uN(x,u)f(u-u')du'$$ $$N(0,u) = \delta (u)$$ Here $f(u)$ is a probability density function for $0 \le u \le u_{max}$, $\int _0 ^ {u_{max}} ...
0
votes
1answer
36 views

What does it mean when fourier/laplace series/transform converges?

I am confused to the differences between fourier and laplace. Searching on the web reveals that they are due to convergence. I am basically confused as to what that means. Additionally, I am confused ...
0
votes
1answer
40 views

Derive Fourier transforms from Fourier expansion. How are they related?

I am just trying to relate Fourier Series expansion to Fourier Transforms. If someone could show how one value on the middle of the table is derived (from expansion) as opposed to deriving their ...
0
votes
2answers
90 views

Why is there an exponential in Fourier's defining integral?

I am having a hard time relating integration with Fourier series. Basically, I just get lost where there is an exponential in the integration to convert into the frequency domain. If someone can ...
0
votes
1answer
40 views

inverse transform of $Z(\omega) =\frac{a}{\alpha-i\omega}$

I am stuck at calculating the inverse transorm of $Z(\omega) =\frac{a}{\alpha-i\omega}$. Can someone help me please? thanks
4
votes
2answers
4k views

Compare Fourier and Laplace transform

I would like to clarify main difference between Fourier and Laplace transforms and also understand if exponential factor is main difference between this two method. So Fourier transform is ...
-3
votes
1answer
100 views

Can you do this Laplace Transform

Can you do this? This is part of my final year EE work. I need to solve this in order to figure out how my sensor is behaving. Please help, and stop down voting. If it is too difficult for you, just ...
2
votes
2answers
304 views

Inverse Laplace of $\dfrac{(s+1)e^{-\pi s}}{s^2 + s + 1}$

Does anyone know how to calculate the Inverse Laplace transform of $\;\;\dfrac{(s+1)e^{-\pi s}}{s^2 + s + 1}\;\,$ ? I've tried it and got (u is the unit step function): ...
3
votes
1answer
74 views

Show that if $L\{F(t)\} = f(s)$ then $L\{F(at)\} = \frac{1}{a} f(\frac{s}{a})$

I'm trying to answer this question and I just don't know how to finish it. I've tried integrating the $te^{-st}$ by parts and then multiplying it by $\frac{1}{a}$ but it doesn't show the answer I ...
0
votes
1answer
314 views

Does a piecewise-continuous function need to be defined at its points of discontinuities?

Is the following function considered piecewise-continuous?? I'm reading conflcting definitions in different places: some highlight that that the function need not be defined at the (jump/removable) ...