Questions tagged [laplace-transform]
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246 questions
-3 votes
2 answers
162 views
Orthogonal signal of u(t) and how they are related in the s domain
I am disatisfied with why we have to pick cosine and sine when doing Fourier analysis of a signal.So I decided that one of my orthogonal signals will be $u(t)$.However what is the orthogonal signal of ...
- 135
2 votes
0 answers
57 views
Non-linear system in s-domain
I am looking a way to predict non-linear systems. Suppose you have a input signal $X(s)$ and a system $H(s)$. If the input signal $$X(s)=\frac{1}{s^{2}+n^{2}} \tag 1$$ ( a (co(sine)) and the system $H(...
- 135
0 votes
1 answer
92 views
Transfer function for a harmonic oscillator
I am solving the damped and forced harmonic oscillator differential equation of motion using a transfer function. The starting differential equation is: $$m\ddot x+ c\dot x +kx =F(t)$$ I took the ...
- 101
0 votes
1 answer
171 views
Absolute integrability and transfer function evaluated at $j\omega$
It's well-known that an LTI system is BIBO-stable if and only if its impulse response $h(t)$ is absolutely integrable: $$\text{BIBO system} \iff \int_{-\infty}^{+\infty} |h(t)|\mathrm{d}t \lt \infty$$...
- 680
0 votes
0 answers
30 views
Is it possible to take Fractional Fourier transform of Laplace transform?
Let $L_t\{f(x, t)\}$ denotes the Laplace transform (two-sided) of $f(x,t)$ with respect to $t$. That is, $L_t\{f(x, t)\}(s)=\int_{-∞}^{+∞}f(x, t) e^{-st} dt$ and Fractional Fourier transform of $f(x,t)...
1 vote
1 answer
80 views
Why is the digital frequency response taken on the unit circle, while the analog is taken along the imaginary axis?
For digital signals, the fourier transform is taken along the unit circle of the Z-transform. The equivalent to the Z-transform in continuous signals is the Laplace transform, but in that case the ...
- 13
0 votes
1 answer
64 views
Is it possible to approximate non-causal time delay?
I have been struggling with a problem regarding a digital control theory. Namely it's a feedforward compensation for a system with a transport delay $T_d$. The problem is that in such a case the ...
- 447
0 votes
0 answers
26 views
How to exploit feedforward compensation for a system with transport delay?
I have a combination of a feedback control loop and feedforward compensation where $\tilde{E}$ represents a fluctuation of the system input (namely a input voltage of a dc-dc converter) which is ...
- 447
0 votes
1 answer
47 views
Confusion about a symbol in Chen's Linear System Theory and Deisgn
In pg. 123 of Chen's Linear System Theory and Deisgn 3rd edition, Theorem (5.2) states: What is the expression after $\sin$? is this a typo? Later he writes, again using this symbol:
- 111
0 votes
2 answers
108 views
What is relationship between the Laplace transform of the ideally-sampled signal and that of the original continuous signal?
Suppose a continuous signal $x(t)$, the Laplace transform of $x(t)$ is $X(s)$. Suppose the ideally-sampled signal of $x(t)$ is $\hat{x}(t)=\sum\limits_{n=-\infty}\limits^{\infty}x(nT)\delta(t-nT)$, ...
- 1
2 votes
1 answer
339 views
How is causality in Laplace transform related to Fourier transform?
Taking the Laplace transform of a system given by a differential equation yields its transfer function $H(s)$. The region of convergence of the causal impulse response of the system lies right of the ...
- 123
0 votes
2 answers
787 views
Relation between the damping ratio and the phase margin in 2nd order systems
I can't remember how to derive the relation between the damping ratio $\zeta$ and the phase margin. I cant remember where to start from to end up with a numerical relationship between them for a ...
- 103
0 votes
1 answer
54 views
Partial derivative of transfer function in Laplace domain
For some LTI transfer function $g(t,\rho)$ with a constant parameter $\rho$, with the transformed equivalent: $$\begin{align} g(t,\rho)&\leftrightarrows G(s,\rho)\\ \end{align}$$ Is it equivalent ...
- 123
1 vote
1 answer
187 views
Don't we need both negative and positive discrete complex exponentials to make a real discrete time signal?
For a continuous time periodic signal , the Fourier spectrum has both negative and positive complex exponentials in equal numbers ,but I have seen for some discrete time periodic signals it is not the ...
0 votes
1 answer
42 views
why we don't get equal number of negative and positive complex exponentials for the DTFS of a discrete time periodic signal?
When we compute the Discrete time Fourier series of a discrete time periodic signal , why don't we get the same number of negative complex exponentials and positive complex exponentials ? Even though ...