# Questions tagged [laplace-transform]

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### 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
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### 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
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### 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
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### 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 ...
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### 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 ...
1 vote
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Suppose that for a system $S$ if we have $t_{2} = t_{1}+t_{0}\rightarrow h(t,t_{2}) =h(t,t_{1})+h(t,t_{0})$ .Then if we take the double Laplace transform to$t,t_{2}$ we will get: $$L_{t_{2}}(L_{t}(h(... • 295 0 votes 1 answer 102 views ### Transfer function h(t) of a positive feedback system I want to find the transfer function h(t) of the below positive feedback system. I came out till this. How can i get the inverse laplace of this function? say β = 1 and γ = 1 3 votes 0 answers 42 views ### Inverting transformation \displaystyle m(t)=\sum_{i=1}^d x(i)^t Suppose there's a vector of d of positive numbers x(1),\ldots,x(d) which I need to obtain from a vector of d derived quantities m(t_1),\ldots,m(t_d) where \{t_i\} is some conveniently chosen ... 3 votes 0 answers 85 views ### Discrete version of this transform? I have the following transform for t>0, a_i>0$$f(t)=\sum_{i=0}^d a_i \exp(-t a_i)$$And I need to invert it for a set of target values b: Find (t_0,t_1,\ldots,t_d) such that f(t_0),f(t_1)... 1 vote 2 answers 793 views ### How we determine type of filter with pole(s), zero(s)? [duplicate] Let's say we have this Laplace transform:$$H_{1}(s)=\frac{1}{(s+1)(s+3)}\;, \; \Re{e} (s)>-1 $$So, we know that there is a poles at s=-1 and s=-3. With these informations, we found that to be ... • 11 1 vote 1 answer 114 views ### Transfer function of LTI causal system I have$$y(n)-3y(n-1)+2y(n-2)=4x(n)-2x(n-1)$$that is the equation for a causal, discrete time LTI system. Using the Laplace Transform I rewrote it as:$$Y(s)-3e^{-s}Y(s)+2e^{-2s}Y(s)=4X(s)-2e^{-s}X(s)...
If I have a system: $$sX(s) = AX(s)+BY(s)+CZ(s)$$ How would I find the transfer functions $\frac{X(s)}{Y(s)}$ and $\frac{X(s)}{Z(s)}$? Do I simply disregard one of the inputs? I am quite confused and ...