# Questions tagged [laplace-transform]

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### How to I get transfer function?

there is a ODE $dx/dt-ax(t)=u(t)$ Firstly, I have to find the transfer function $u$ to $x$ using exponential input. So I put $u(t)=e^{st}$ to the ODE, and I got $x(t)=x(0)e^{at}+1/(s-a)e^{st}$. In ...
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### Confusion in property of Z transform of ideal sampled waveform

I was reading about z transfom of ideal sampled signals and one of the properties of Z transform of sampled signal that surprised me,here it is (image) So here this property of Z transform is quite ...
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### Real impulse response

It will be great if someone can explain me what exactly means "real impulse response". Further more , what is the effect of such a response on ROC (Laplace plane) and in particular if its ...
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### Fourier Transform of an Exponential Sine Sweep

The Exponential Sine Sweep (ESS), according to Farina , can be described by the following formula: $$x(t)=\sin\left(\frac{2\pi f_1 T}{R}\left(e^{\frac{t R}{T}} -1\right) \right)$$ where, $t$ - ...
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### Confusion in initial condition of differential equation using Laplace transform transform

I'm confused in solving linear constant coefficients differential equations (LCCDEs) by Laplace transform if initial conditions are given at time just before $t=0$ just after $t=0$ exactly at $t=0$ ...
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### Impulse response if initial conditions are given

In most books, impulse response of LTI systems are calculated by assuming initial rest condition, but how to calculate response of an impulse input if there are some initial conditions present ? My ...
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### How can I find the transfer function of the following block diagram?

I've the following image and I want to find the transfer function from input $x(t)$ to output $y(t)$. I know that I have to apply Laplace Transform, so the integrator becomes $\dfrac{1}{s}$, but I don'...
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### How to compute transfer function $G(s) = \exp \left( - \sqrt{s} \right)$ in Matlab / Simulink?

How to compute transfer function $$G(s) = \exp \left( - \sqrt{s} \right)$$ in Matlab / Simulink? I am trying to calculate a PID controller for this function. This function describes heat transfer via ...
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### Compute output given input, transfer function and initial conditions

The problem statement is Consider a causal LTI system whose transfer function $H(s)$ is given as $$H(s)=\frac{s+2}{(s+3)(s+4)}$$ Compute the output $y(t)$ for an input $x(t)=e^{-2t}u(t)$ when $y(0)=1$...
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### Names of system functions in frequency domain

I was just trying to refresh my systems theory known from long ago, and I realized that I had forgetten the name of the basic functions. Specifically, what are the names of these functions ...
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### Apply Transfer Function in Continuous Domain in Matlab

I have the coefficients of a transfer function (i.e. numerator and denominator) in Laplace domain. How can I apply this to an input waveform using MATLAB script? I am looking for a function or piece ...
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### How to know basics about convergence

I apologize if the post is incorrect. I'm a sophomore student studying Electrical engineering. As a part of an introductory course on signal and linear systems, I'm required to learn Fourier and ...
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### What are the missing steps in the derivation of this equation?

I am trying to understand the model of a piano hammer described here. The relevant excerpt is: As I understand it, they are saying in (12a) that if the hammer spring's uncompressed end's y position ...
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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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### 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 ...
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 ...