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Questions tagged [laplace-transform]

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How do bode plots work with unstable systems work?

If I had a system with right-half s-plane poles, how would a frequency response work? Since a purely imaginary value for s, would cause the Laplace transform to diverge for such a system, what meaning ...
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Is there an analogy of the Fourier-decomposition in the Laplace space to decompose a signal to a few components?

I have a signal from which I know, that it is the sum of a few, exponentially decaying components. I want to find these components. If it would be a sum of some sinusiod waves, it would be easy to ...
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23 views

System Response Terminology

If I have a system specified by $$P(D)y(t)=Q(D)x(t)$$ and I specify initial conditions $y(0^-)=a, \ y'(0^-)=b,\ x(0^-)=c$ does the term $x(0^-)=c$ correspond to the zero state response or zero ...
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57 views

From Fourier transform to Laplace Transform

It's well known that you can estimate the Fourier Transform $X(f)$ of a signal $x(t)$ via its Laplace Transform $X(s)$, just by setting $s = j2\pi f$ to the latter, as long as the region of ...
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Using laplace transform to find the expression for voltage in the circuit

Let's say we have the following circuit: Generator in the circuit has sinusoidal waveform $u_g(t)=\sin\omega t$. Other known values: $ L=0.25H\\ R=1\Omega \\ C=0.5F \\ \omega=1 \frac{rad}{s} \\ k=1$ ...
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34 views

Inverse Laplace transform of two-sided and one-sided Laplace transform

As I read in Wikipedia, there are two types of Laplace transforms One-sided Laplace transform: $F(s) = \int_{0}^\infty e^{-st} f(t) dt$ Two-sided Laplace transform: $F(s) = \int_{-\infty}^\infty e^{-...
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confused about time shifting property of Laplace Transform

In book signals and systems 2 edition a question is given which is as follows: $$ x(t)=e^{-3(t+1)}u(t+1) $$ and we are asked to find the unilateral Laplace Transform of the signal. The ...
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110 views

Can a Fourier Transform exist even if the j$\omega$ axis is not in the Region of Convergence in it's Laplace Transform

A couple of confusions have been occurred. The Signal I'm considering is f(t) = sin(t)*u(t) Fourier Transform of it can be derived. $-i \pi (\delta (\omega -1)-\delta (\omega +1))$ According to my ...
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1answer
48 views

How to find the coefficients of the following differential equation

An arbitrary signal $v(t)$ pass through the following system, $w'(t) + 5 w(t) = v'''(t) + 320v''(t) + 40 v' (t) + 40v(t)$ How to determine the coefficients of the following differential equation, ...
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1answer
65 views

Determining the causality of a signal with it's pole-zero plot

I have the following question: Pole-zero plot of x(t) and y(t) are given below: The signal $g(t)$ and $h(t)$ are defined as $g(t)=x(t)e^{-3t}$ and $h(t)=y(t)*e^{-t}u(t)$. If $g(t)$ ...
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What is wrong with my residue partial expansion method? (Transfer Function into State-Space Modal/Diagonal Form)

I'm using reference from here and here. This is Laplace transfer function of DC Control Speed System: $$\frac{\omega(s)}{V(s)}=\frac{K}{(Js+b)(Ls+R)+K^2}$$ Where, $\omega$ is the motor angular ...
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1answer
1k views

blur detection using opencv

I'm writing a script to detect blur images using OpenCV by applying Laplacian filter and calculate the std but there is a problem the std for images that contain motion blur is very close to those ...
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1answer
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Bilateral Laplace transform and existence of Fourier transform

I was reading from Athanosios Papoulis' "The Fourier integral and its applications." and they referenced the bilateral Laplace transform and Fourier Transform as: $$F(p)=\int_{-\infty}^{\infty}e^{-pt}...
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How does this digital signal controlling a switch in the circuit affect the output voltage?

Suppose you have a circuit which has the input signal $x(t)=2\sin (ω_ot + \pi/6)$. The switch in the circuit is controlled with a digital signal of the form: $s(t)=\sum_{k=-\infty}^{+\infty} (u(t+ε-...
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3answers
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Why use transfer functions than differential equations?

I have some simple questions regarding DSP and Control Systems, but found no simple answers. I just need simple and easy to understand answers, not complex answers with huge maths. Why we use ...
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How to find transfer function of a logarithmic or power function?

I'm dealing with logarithmic system $\log_{10}(y(t)) = m \log_{10}(x(t)) + b$, and I need to find the transfer function, $Y(s)/X(s).$ What is the Laplace transformation of $\log_{10}(f(t))$? What I ...
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2answers
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Characteristic and moment generating function of a random variable interpretation

I have been studying about moments and cumulants of a random variable. Even though the definitions of characteristic and moments generating function are very similar (only the sign in the exponential ...
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1answer
137 views

Where does this star came from? [EDIT - Detailed Question]

First of all, it's a rare topic in google, so I can't find intuitive explanation about step-invariant, so I don't understand actually what it is, except to solve zero order hold transfer function. In ...
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3answers
237 views

Transfer function of a frequency shifting system

There is a system which shifts frequencies of input by -Fc such that: Y(S) = X(S).H(S) But X(S) has value zero from 0 to Fc. I am confused on how the product of X(S) and H(S) becomes a positive ...
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How to transform a Fractional Order Laplace Transfer Function into a digital filter?

I'm working with loudspeaker impedance analysis. Electrical behavior of loudspeakers can be modeled with RLC networks. But real loudspeakers have components, that exhibit some non-linear and frequency ...
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What are the advantages of Laplace Transform vs Fourier Transform in signal theory? [duplicate]

What are the advantages of Laplace Transform vs Fourier Transform in signal theory?
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1answer
235 views

Servo motor analysis

I'm studying a mathematical behaviour of a servo motor and I need some help to understand it. The output signal is $\beta(t)$, representing the angle rotated by the axis at instant t, in relation to ...
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1answer
457 views

Relating transfer functions with step responses

Relate the transfer function to its' corresponding step response. First, I tried setting up the poles and zeros of the transfer functions. This helped a bit since I know that $G_A (s)$, $G_B(s)$ and $...
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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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3answers
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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 ...
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1answer
463 views

Bilinear transformation confusion

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=\...
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2answers
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Why do poles in the left half of the S plane make a system stable?

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 ...
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1answer
37 views

How can I translate what I have learnt in Transfer Functions to differential equations?

I have gone through the entirety of K. Ogata's Modern Control Engineering, and I do not understand how can I translate all the transfer function models into differential equations? For example, how ...
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1answer
310 views

Meaning and unit of frequency in Laplace (Fourier) transform

Imagine transfer function obtained by Laplace transform, for example: $G(s) = \dfrac{1}{s+1}$ Now, I would like to do some frequency analysis, so I replace the $s$ with $\omega i$ (let's consider ...
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1answer
60 views

Laplace of step and integration are same?

Why do we have Laplace transform of a step function and integrator is same. \begin{align} \mathcal L\left[u(t)\right] &= \frac 1s\\ \mathcal L \left[ \int dt\right] &= \frac 1s \end{align}...
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LTI system with Laplace transform

Given the input $$x(t)=u(t)$$ and the corresponding output signal measured as $$y(t)= 2 e^{-3t} u(t)$$ determine the impulse response $h(t)$. This what have done so far: $$ h(t)= \mathscr{L}^{-1} \...
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165 views

How is the simplified version of the Bromwich inverse Laplace transform integral derived?

I do not understand how the last equality is derived from the previous. Apparently the first term in the integral (involving $\mathrm{cos}$) is equivalent to the second (involving $\mathrm{sin}$)!! ...
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1answer
193 views

Impulse response of a continuous system sampled with zero-order hold

I've a continuous system $$F(s) = \frac{K}{Ts+1}.$$ I sample it with zero-order hold with sampling period $T_s$. The discrete system transfer function is $$ \begin{aligned} G(z) &= % \frac{z-1}{z}...
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Laplace Transform of $f(t+a), a>0$ where $f(t)$ is not periodic

For $a > 0$, is there any known representation of the Laplace transform of $f(t+a)$ in terms of the Laplace Transform of $f(t) $ Note: In my application, $f(t)$ is not a periodic function and the ...
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1answer
862 views

First derivative analog filter

I'm reading about fault detection via signal processing in time domain. One possibility is to check that first derivative of the signal is in some predefined bounds. The text says that to obtain the ...
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1answer
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Find transfer function from root locus and step response diagram?

I am given the response of a step of magnitude of 3 and the root locus and I have to find the transfer function of the system. The function I find gives me the step response(magnitude of 3 again) of ...
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2answers
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A question about the meaning of pole in time domain

Lets say I have a transfer function $H(s)$ of a system defined in $s$-domain as: $$H(s) = \frac{1}{s - (-1-j)}$$ So I conclude that the pole on the $s$-plane is where $s = 1+j$. So far so good. Now ...
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1answer
958 views

How can I plot a 3D graph of a given Laplace Transform of a function?

Let's say I have a function called $f(t)$ in time domain as: $$f(t) = \exp(-3t)\cos(5t)$$ And the Laplace transform of this function call it $F(s)$ becomes: $$F(s)=\frac{(s + 3)}{(s + 3)^2 + 25}$$ ...
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On the meaning of s-plane and it's link to a transfer function

Considering Fourier analysis and let's say I'm walking on the blue frequency axis in the below 3D plot from zero towards infinity: So each time I encounter a non zero blue bar, I check the frequency ...
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2answers
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Laplace transform of product of signal and impulse train

I'm reading 'Discrete Time Control Systems' book by Ogata and came across a few statements (specifically, (3-1) and (3-2)) which I have not been able to understand. It is said that any continuous ...
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1answer
806 views

Causal Signal - Fourier Transform or Laplace Transform

I am dealing with a physics problem which is related to signal processing. The problem requires me to calculate the instantaneous force acting on a body which depends on some physical parameter $x$. ...
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1answer
54 views

Why do these 2 methods give different solutions?

I need to solve what is underlined in red for $x_i$, nut currently I'm interested in the right side of the equation only. On the left I sarted by doing the Laplace transform of $x_u'$ and $x_u$, and ...
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Laplace transform of $f\left(\frac{t - b}{a}\right)$

Consider the function $f\left(\frac{t - b}{a}\right)$. We want want to calculate its Laplace transform. There are two approaches: Firstly, let $g(t) = f\left(\frac ta\right)$. Then $\mathcal{L}\...
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291 views

How to find analytic description of filtered signal

I am looking for an exact analytic description of a filtered signal. I have an electronic circuit whose input is a monoexponential decay. First (1) the signal gets filtered by a simple RC-Lowpass. ...
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Control systems and convolution

I think i am not understanding the concept of convolution well. Lets say we are given a system impulse response in the S-domain, and we have implemented a controller $G_c(s)$ that will adjust the ...
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Feedback systems & oscillations

The transfer function of feedback system is: $$ \frac{V_{\rm out}}{V_{\rm in}} = \frac{A}{1+Af} $$ Where $A$ is the open loop gain, and $f$ is the feedback gain. Now for oscillation to happen, $Af$ ...
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891 views

Laplace Transform of Cosine, Poles and Mapping to Frequency Domain

I am trying to understand the connection between Laplace transform ($s$-plane), and frequency domain calculation. Let's take the Fourier transform of $\cos(\omega_0t)$, which equals to $\pi[\delta(\...
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1answer
162 views

Find state space model from transfer function

Let's suppose we have: G(s) = (s+1)/(s^2-2s+1) how can we find the state space representation of the transfer function: x_dot = x2 x2_dot = 2*x2-x1+u where u is an arbitrary input. I am very new ...
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Why does the separable filter reduce the cost of computing the operator?

A separable filter in image processing can be written as product of two more simple filters. Typically a 2-dimensional convolution operation is separated into 2 onedimensional filters. This reduces ...
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How can a system be unstable if $L(j\omega)$ is never exactly $-1$?

Say we have a linear system with unity feedback, with loop transfer function $L(j\omega)$. The closed-loop transfer function from reference to output is $T(j\omega) = \frac{Y(j\omega)}{R(\omega)}=\...