# Questions tagged [laplace-transform]

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### s-Domin or z-Domain - What to Use for Mixed systems

I recently had to deal with a power electronic system where I had to implement a dynamic model of a power converter in order to design a suitable controller for that converter. The control will be ...
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### Help with my first (simple) Z-transform

I need to transform this Laplace function to the z-domain: From the answer I received: $s=(1-z^{−1})/T$ Then substitution into my Laplace function would give: $t(z) = 2R/(m*(1-z^{−1})/T + 2R)$ Is ...
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### How do I convert this simple Laplace equation to Z-domain?

A basic model of coupled strings (eg. piano) is provided here as: The principle is that it has two identical string simulations each formed by a delay line and LPF. The outputs of these are summed at ...
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### Why the unilateral Laplace transform?

Why is the Laplace transform commonly taught as the unilateral Laplace transform? I mean, for the Fourier transform, we commonly have the bilateral transform... if the signal is 0 for $t<0$, then ...
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### Solving the system response using inverse Laplace transform

I am trying to solve this question but I got stuck when inverting the Laplace transform for this problem. I do not know that whether I do it right or wrong. Moreover, I do not know how to handle the ...
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### Inverse Laplace Transform

A system given by $\frac{s-1}{(s+1)(s-2)}$ has to be inverse transformed so that it is anticausal and nonstable. The answer given is $h(t)=-\frac{1}{3}(2e^{-t}+e^{2t})u(-t)$ Why the minus sign at the ...
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### Determining Stability of a continuous time system using Laplace Transform

I'm following Oppenheim's book. In exapmles, the laplace transforms of of the following signals $e^{-t}u(t)$ and $e^{-t-1}u(t+1)$ is given as $\frac{s}{(s+1)}$ and $\frac{e^{-s}}{(s+1)}$ both ...
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### What is the inverse Laplace transform of squared denominator term?

Referring to the image below, what would the inverse Laplace transform be? I can't seem to find any tables that include this case.
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### Z transmittance from diffrence equation made out of diagram

I have a problem with getting Z transmittance out of a single block of diagram, when e(nT) is as an input, and u(nT) is as an output. Period of sampling is T = 0.5 s The diagram is: My first thought ...
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### Why Are There Two Different Common $3 \times 3$ Kernels for the Laplacian?

I find both of these 3x3 Laplacian kernels to be commonly used: 0 -1 0 -1 4 -1 0 -1 0 and: -1 -1 -1 -1 8 -1 -1 -1 -1 ...
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### Why do convolution kernels such as Gaussian, Laplacian, LoG almost always seem to be expressed in integers?

I'm a total newb in search of some deeper understanding, but I'm not able to read the maths behind these on Wikipedia. If I understand correctly, you get the new value for each pixel by multiplying ...
61 views

### Step response of third-order continuous-time transfer function

I have a transfer function of the form: $$H(s) = \frac{b\omega_n s^2 + a\omega_n^2 s + \omega_n^3}{s^3 + b\omega_n s^2 + a\omega_n^2 s + \omega_n^3}$$ If it matters, $a=b=2$. Is anyone aware of ...
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### How can the Poles of the Root Locus be negative?

My understanding of drawing a root locus diagram is that stability requires all roots of the characteristic polynomial of the open loop transfer function to lie in the negative real part of the plane. ...
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### Difference between the two forms of input-output relationships of an LTI system

$$y(t)=f(t)*h(t)\tag{1}$$ $$y(t)=H(s)e^{st}\tag{2}$$ $$H(s)=\int_{-\infty}^{\infty}h(t)e^{-st}dt\tag{3}$$ Let $f(t)$ in Eqn $(1)$ be $e^{st}$. In many worked out examples, I have found that the two ...
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### Laplace transform of a finite duration signal

Consider the following signal: $$x(t) = e^{-2t}[u(t) - u(t-5)]$$ This signal exists only from 0 to 5 time units. Elsewhere, it is zero. Now, let's find the laplace transform of this signal using ...
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### Why there is Difference between shapes of ROC of z domain and s domain?

ROC(region of convergence) of Z domain is shown by a circular region while ROC in S domain is shown by a rectangular(approximately looking like rectangle) region What is the reason of this difference ...
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### Why not use a complex number in the exponent in the z-transform?

I am trying to comprehend how the z-transform has come to be similar but different from its continuous counterpart, namely the Laplace transform. It seems to me that the most parallel and intuitive ...
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### Basic difference between Fourier transform and laplace transform? [duplicate]

I have read few links about difference between Fourier transform and Laplace transform but still not satisfied Please correct me if i am wrong Simply put, the main difference between Fourier ...
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### Laplace transform of a time domain sampled data MATLAB

I have two sets of one second voltage data sampled with 4000Hz and I can plot all the voltage points vs time points in MATLAB. So it means I have a data matrix with with length of 4000 one column for ...
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### How to compute the Laplace transform of a discrete signal?

Assume I have a discrete random signal, $f(t)$ for which I want to calculate the laplace transform. How can I do it in matlab without using sym variables, for ...
Wikipedia says in bilinear transformation from \$s\$ domain to $z$ domain relation is $$\boxed{s \longleftarrow \frac{2}{T}\frac{z-1}{z+1}}$$ But here this relation is given like this \boxed{w=\...
A point on the S-plane (where $s=\sigma+j\omega$) represents a signal with a given frequency (given by the imaginary component) and which either decays, increases or stays stable (depending on the ...