Questions tagged [laplace-transform]
The laplace-transform tag has no usage guidance.
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Bode plot phase shift equation when poles and zeros are not at the origin
Let $$H(s)=\frac{s^{n}}{s^{m}}$$
For $n \ne m$ the phase shift between output and input will be
$\frac{\pi}{2}(n-m)$.
For situations where the poles and zeros are not at the origin, I could find the ...
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Mixer and control systems
A mixer in the time domain usually multiplies 2 signals of the time domain , however what does it do in the Laplace domain?Is there a equivalent block diagram of a mixer in the Laplace domain?The ...
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Simulate Op-Amp low-pass transfer function in Python
I am struggling to simulate the frequency response of a simple op-amp low-pass transfer function in Python. The results I get are not accurate. The transfer function is $H(s)=\frac{1}{1 + s\tau}$, ...
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I have a transfer function in s domain convert to time domain
I have a transfer function of $\frac{1}{s^2}$ in $s$ domain that represents a $\frac{\text{output}(s)}{\text{input}(s)}$.
Say I put a constant DC input as input (s) or just input in time domain that ...
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Equipment to test my theory on time varying systems
How can I make a linearly time varying system to test my theory?
Can I ask for a PID microcontroller available from my university such that $K$ is gradually increased from 0 to $c$
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Correlation gives contradictory results
I am trying to find the correlation between the signals $u(t)$ and $\sin(t)[u(t)-u(t-2)]$
The correlation function $C(t) = \int^{\infty}_{-\infty} u(\tau+t)\sin(t)(u(t)-u(t-2))d\tau$
This is my ...
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Derivation of 9 point Laplacian filter
I'm reading a paper on how construct isotropic laplacian filter, and perhaps because it's an old paper, the notation in it really bothers me a lot. So can someone please explain it to me? For example, ...
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Is there a Fourier Transform generalization that lets you analyze arbitrary complex frequencies?
Suppose you have a function that can be described as $$f(s) = \sum_{n=0}^{\infty} a_n e^{f_n s}$$ where each $f_n$ is a complex number. I am looking for a transform $T$ to act on $f$ which produces a ...
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How to separate Transient and Steady-State Expression from Periodic Summation Response?
Background
My question comes from here, it's a response of 1st order LPF RC circuit from an arbitrary periodic input.
How to determine the transient response of a circuit to causal periodic inputs?
...
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Laplace domain transfer function from system sampled at discrete times
I'm trying to understand an analysis of a sampled continuous time system in the Laplace domain. The source analysis is here (PDF page 6, slide marked 11); I'll explain further below. Suppose I have a ...
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Finding the region of stability of a system
Suppose we have a closed loop system controlled by some microcontroller $K$
First we take the open loop gain which is $\frac{K}{s(s+6)}$.It has 1 pole at the origin and at $s=6$ and 0 zeros.
So we ...
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Calculating transfer function of a linear time varying system?
If we excite a LTI system with the Dirac delta $\delta(t)$, the system outputs the impulse response $h(t)$. For a LTI system, it doesn't matter when we excite the system with the Dirac delta, we will ...
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Max input of a system given it's transfer function and an assumed step change (beginner)
I have an exercise that gives me the following transfer function
$$
\frac{0.5}{s+0.5}
$$
and an assumed step change in the target of 20
I am asked to calculate the maximum input for the assumed step ...
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LLTV Systems breakdown(2)
In this question I proved that for a linear linearly time varying system $S$ such that if $t_{2} = t_{1}+t_{0}$ then $h(t,t_{2}) = h(t,t_{1})+h(t,t_{0})\rightarrow$ $h(t,t_{0}) = g(t_{0})h(t) $ where $...
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What exactly are the assumptions behind Tustin's formula? Application on state space models
I was parsing the forum when I saw this post surging out of the depths of this forum like an old Kraken. The problem is quite simple.
You have a continuous time state space model :
$$
\begin{split}
\...
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Linear linearly time varying systems Laplace transform
Suppose that for a system $S$ if we have $t_{2} = t_{1}+t_{0}\rightarrow h(t,t_{2}) =h(t,t_{1})+h(t,t_{0}) $ .Then if we take the double Laplace transform to$t,t_{2}$ we will get:
$$L_{t_{2}}(L_{t}(h(...
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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
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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 ...
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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)...
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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 ...
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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: $$Y(s)-3e^{-s}Y(s)+2e^{-2s}Y(s)=4X(s)-2e^{-s}X(s)...
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Finding transfer functions from a system of multiple inputs
If I have a system: $$sX(s) = AX(s)+BY(s)+CZ(s)$$ How would I find the transfer functions $\frac{X(s)}{Y(s)}$ and $\frac{X(s)}{Z(s)}$?
Do I simply disregard one of the inputs? I am quite confused and ...
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How does the state estimate selection work?
I have been solving following problem. I have two open loop state estimators used for estimation of the unmeasurable states of a given linear dynamic system. The first estimator provides estimate $\...
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First Order State Space Question
I am trying to understand the state space equation for a simple first-order LTI system. Suppose I have a system with impulse response
$$h(t) = \frac{1}{\tau}e^{\frac{-t}{\tau}} \ \theta(t)$$
In this ...
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Does the definition of stable system contradict itself?
A system is said to be stable when any of its poles are <0.
However I don't get why that is the case. Negative poles mean negative angular frequency, and negative angular frequency is equal to ...
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What is the intuitive interpretation of the transfer function of this system?
If I have the system that could be observed in the next Image:
I want to know the transfer function, where the external force $f$ is the entry and $x_1$ is the output. The direction and positive ...
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Transfer function and Laplace domain
If we give a input $x(t)=u(t)$ to a system $\mathcal{S}$ we get an output $y(t) = e^{-t} u(t)$.
After we Laplace-transform both the input and the output we get the transfer function
$$H(s) = 1-\frac{1}...
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Name of property of Laplace transform
\begin{align}
L[e^{-at}u(t)] &= \frac{1}{s+a}\\
L[\cos(\omega_{o}t)u(t)] &= \frac{s}{s^{2}+\omega^{2}_{o}}\\
L[e^{-at}\cos(\omega_{o}t)u(t)] &= \frac{s+a}{(s+a)^{2}+\omega_{o}^2}
\end{...
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Sampling with impulse train
There are many times when the textbooks used by all university students like me make an introduction to the notion of sampling of a continuous-time signal with an impulse train as shown below.
Why do ...
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Prove that the filter is stable, causal and minimum phase
I have a system which has the following transfer function
$$H(s)=\frac{\beta + s}{s^{2} + 2\alpha s + \beta^{2}}$$
where $\beta = \sqrt{\omega^{2} + \alpha^{2}}$ and $\alpha>0$.
This system, as ...
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Study the stability of $H(s)=\frac{\beta + s}{s^{2} + 2\alpha s + \beta^{2}}$
I have a system which has the following transfer function
$$H(s)=\frac{\beta + s}{s^{2} + 2\alpha s + \beta^{2}}$$
where $\beta = \sqrt{\omega^{2} + \alpha^{2}}$ and $\alpha>0$. The degree of ...
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What is the Laplace Transform of the output power spectrum if the input signal is a white noise?
Let us consider a random wide-sense stationary process $n(t)$, which passes through a filter $h(t, \tau)$. Its autocorrelation function is
$$R_{n^\prime}(t)=\int_{-\infty}^{\infty} \int_{-\infty}^{\...
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Reference for Wiener-Kolmogorov whitening procedure
In an old paper, accessible only for a fee, I found:
(where the LHS of Eq (5) lack the symbol of derivative). What is the Wiener-Kolmogorov whitening procedure? I would like to study this procedure, ...
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How does the phase/gain margin method work?
We have the closed loop transfer function:
$$T(s)=\frac{L(s)}{1+L(s)}$$
So as far as I understand we check along the $j\omega$-axis on the Bode plot whether $L(s)=-1$, cause that's when $T(s)$ has ...
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Time invariance in transfer functions
I read this in a book:
here ${\cal L}[x(t-a)u(t-a)]$ is the laplace transform of a time shifted function $x(t)$ shifted by $a$ seconds and we know that transfer functions have the formula $H(s)=Y(s)/...
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Finding and displaying Laplace or Z transform ROC(region of convergence) using MATLAB
Is there any way, we can use MATLAB for finding and displaying Laplace or Z transform Region of convergence?
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Confusion regarding Laplace transform calculation in MATLAB
I am trying to learn about Laplace transform and especially about ROC and i found out on this weblink.
I have also attached a snapshot of this link and highlighted where it is being said that although ...
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making a laplace s-domain plot from numerical data to decompose signal into decaying sinusoids
I would like to make a 3D laplace s-domain plot from experimental data I have. The examples I have seen for this are when the function is already known and an analytical solution can be obtained (...
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Laplace transform of derivative
Here is a short proof that Laplace Transform of $x'(t)$ is Laplace transform of $x(t)$ multiplied by s:
On the other hand, the proof that I know uses integration by parts:
One condition for the ...
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Bandwidth of a given function
Suppose the signal given is $x(t)=(cos(5t)+e^{-2t})u(t)$ and the goal is to find the bandwidth of this signal. We know the bandwidth, $B$, is just $f_{max}-f_{min}$.
Our first step is taking the ...
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Product of Doublet and Arbitrary Function
We know that the product of the delta function and another function samples the latter function. That is,
$$
\delta(t-\tau)f(t)=\delta(t-\tau)f(\tau)
$$
Does the doublet function retain this same ...
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Step response of a given input and output (Laplace or Fourier)
I am trying to calculate the step response of the following given:
Should I use Laplace transform or Fourier transform?
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Filter filters out more than needed
I am currently coding a school assignment. I have a 1.5s recording of someone's speech that has 4 rogue cosines mixed in. With sampling rate 16000Hz, I divided the recording into frames of 1024 ...
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The Laplace transform - Steven W. Smith Book - impulse response cancellation method
While studying the Laplace transform using Steven W. Smith Book I found something uncomprehending. In the 32th chapter - The Laplace Transform, page 590, last paragraph describes the cancelling ...
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What will the output of a system which has no Fourier transform?
Let's assume a system $h(t)= e^{j2t}$. This system has no region of convergence. What will be the output if I provide any input to this system?
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Confusions regarding differences between Fourier transform & Laplace transform?
Although this topic has already been addressed in multiple popular questions of SE but i have few confusions in this regard
Number 1)
Link of question
https://electronics.stackexchange.com/questions/...
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Are there any examples of "Causal" Continuous-Time Linear-Time-Invariant Systems (CT-LTI) with output given by finite-duration functions?
Are there any examples of "Causal" Continuous-Time Linear-Time-Invariant Systems (CT-LTI) with output given by finite-duration functions $y(t)$??
With output I am meaning that $y(t)$ is such ...
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How are pole-zero plots, magnitude response plots, and phase response plots related?
Given that the Laplace transform of a continuous-time signal $h(t)$ is $H(s)$, what can a plot of the poles and zeros of $H(s)$ on the $s$-plane tell me about the magnitude response and phase response ...
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Connection from Fourier to Laplace Transform
I have a basic understanding of Laplace and Fourier but having trouble making a connection. Every time I attempt to look at reasons these are connected I'm told about the s-plane and regions of ...
