Questions tagged [laplace-transform]

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20 views

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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1answer
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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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2answers
330 views

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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237 views

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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23 views

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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1answer
24 views

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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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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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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2answers
2k 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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3answers
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How poles are related to frequency response

I have recently fallen into fallacy, considering pole s=1 as there is infinite response at frequency 1. Yet, response was only 1. Now, can you derive the frequency response, given the poles? ...
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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 ...
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1answer
27 views

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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27 views

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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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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1answer
29 views

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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1answer
507 views

Questions related to Laplace Transform

While studying Laplace transform, I also some questions which I want to understand: a) We used to say that Laplace transform include both real and imaginary part whereas in Fourier transform we ...
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215 views

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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1answer
79 views

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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1answer
51 views

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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48 views

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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2answers
131 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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709 views

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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1answer
36 views

Why does subbing $s = j\omega$ into the Laplace transform of a cosine wave yield a purely imaginary result?

The Laplace transform of a cosine starting at $t=0$ is given by $$F(s) = \frac{s}{s^2 + \omega_0^2}$$ If I sub in $s = j\omega$, I get the Fourier transform of a cosine starting at $t=0$: $$F(j\...
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What is difference between natural response and zero-input response of a system and how to find natural response? [duplicate]

In most books it is said that natural response is another name to zero-input response while in some resources is is mentioned that the classification is based on poles of transfer function and input....
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1answer
192 views

Output of an LTI system given its transfer function and input

Given the transfer function $$T(s) = \frac{100}{1 + \frac{s}{10^{6}}}$$ and the input $$v_i(t) = 0.1 \sin(100t)$$ find the output, $v_o(t)$. My approach was to use $v_o(t) = \mathcal{L^{-1}}\left\{T(...
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33 views

Region of convergence of transfer function

I posted this question Mathematics SE and got no answer so I have posted it here. I learned in my signal processing class that an LTI system can be defined using a linear constant coefficient ...
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1answer
32 views

Time Setting of $z$ and Laplace Transforms

I'm aware that the z-transform and the Laplace Transform have an analogous relationship but I want to be doubly-sure that the z-transform only works in discrete-time and that the Laplace transform ...
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1answer
47 views

Why is the ROC of Laplace transform independent of imaginary part of s?

An integral is defined as converging if it yields a finite value upon application of limits of integration. It is divergent otherwise. Now sticking to the mathematical notation of Laplace transform, ...
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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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1answer
90 views

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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33 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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137 views

Confusion Regarding Bi Linear Transform

I was reading my book where the z-transform of a signal is derived to be ${1-e^{-2bT}z^{-1}}$ . Then it goes on to say that by applying the bilinear transform we can get $$\frac{2(1+bT+(bT-1)z^{-1})}...
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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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1answer
232 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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1answer
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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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1answer
201 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
58 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
190 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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1answer
332 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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1answer
145 views

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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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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2answers
73 views

Why we take Laplace Transform of functions which converged using Fourier Transform

There are several functions for which we know that Fourier Transform will exist but still we calculate its Laplace Transform. Can I know the reason why we need to take Laplace transform for which we ...
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1answer
87 views

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
367 views

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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1answer
521 views

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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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 ...