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# Questions tagged [laplace-transform]

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### ROC of the function in the problem 9.14 of Oppenheim's Signals and Systems textbook

I have solved the problem 9.14 in Oppenheim's Signals and Systems textbook, but my solution and the one in Slader is different. Problem is given above. And Slader solution is here. I have also ...
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### Response of an ideal integrator to a cosine wave

It sounds like a very elementary question on system theory but I got quite confused about it, so hopefully you guys can enlighten me. I'm considering an ideal analog integrator, i.e., a system with ...
25 views

### Derive the Forward Euler substitution for transfer function

In the book "The control handbook. Volume 1 " by Levine, the author shows that the transfer function: can be aproximated and discretized in the transfer function: using the forwar euler integral ...
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### Proof of Forward Euler for discretizing a transfer function

In Levine book "The control handbook" it is shown that, for discretizing a transfer function $\frac{1}{s}$ using Forward Euler i simply have to replace s with $\frac{z-1}{T}$. How can extend the ...
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### Forward Euler Discretization

I don't understand why the substitution $s=\frac{z-1}{T}$ allows us to discretize a transfer function from laplace to z-transform through Forward Euler Discretization. Can you explain to me ?
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### Anyone explain to me this video?

I was watching a video in time 24:48 I would like to know where you got the value .9 (1.14z + .941) and 1.0232 + .757 Does anyone explain how he got those numbers?
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### Why does the solution for the voltage of this RLC circuit result in a maximum capacitor value?

I have a circuit with an inductor (L), capacitor (C), and two resistors (R1=R2): This represents an equivalent electrical circuit to a plectrum or hammer (cap=spring, inductor=mass) striking a string ...
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### What did I do wrong with this simple filter build?

I tried to put everything I have learned from people here together to code my first filter from scratch. Unfortunately, it didn't go well and I'm not getting the expected output. The math/code became ...
59 views

### 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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### 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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### How to convert from Laplace Domain to Time Domain?

I want to convert the following equation from Laplace domain to continuous time domain: $F(s) = \frac{-2 m k v R}{2 m R s^{2} + m k s + 2 k R}$ m, k, v, R are all constants. If I can factor or put ...
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### What does z^(-1) represent here?

I understand that when you have a Laplace function, you can do a bilinear or forward/backward Euler substitution for $s$ to phrase it in terms of $z^{-1}$. In a typical filter, $z^{-1}$ represents the ...
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I am trying to understand this equation: It comes from: $Force = mass * acceleration$ $F(t) = m * a(t)$ $F(s) = m * (s^2 * y(s) - s*y0 - y0)$, where $y0=0$ $F(s) = m * s^2 * y(s)$ $y(s) = F(s)/(... 2answers 226 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,$Af$... 1answer 40 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 ... 0answers 22 views ### 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 ... 1answer 47 views ### 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 ... 2answers 346 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 ... 1answer 257 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 ... 0answers 24 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 ... 1answer 26 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 ... 2answers 52 views ### Why Are There Two Different Common$ 3 \times 3 $Kernels for the Laplacian? I find both of these 3x3 Laplacian kernels to be commonly used: 0 -1 0 -1 4 -1 0 -1 0 and: -1 -1 -1 -1 8 -1 -1 -1 -1 ... 1answer 57 views ### How can the Poles of the Root Locus be negative? My understanding of drawing a root locus diagram is that stability requires all roots of the characteristic polynomial of the open loop transfer function to lie in the negative real part of the plane. ... 2answers 2k views ### blur detection using opencv I'm writing a script to detect blur images using OpenCV by applying Laplacian filter and calculate the std but there is a problem the std for images that contain motion blur is very close to those ... 3answers 26k views ### How poles are related to frequency response I have recently fallen into fallacy, considering pole s=1 as there is infinite response at frequency 1. Yet, response was only 1. Now, can you derive the frequency response, given the poles? ... 3answers 87 views ### Why do convolution kernels such as Gaussian, Laplacian, LoG almost always seem to be expressed in integers? I'm a total newb in search of some deeper understanding, but I'm not able to read the maths behind these on Wikipedia. If I understand correctly, you get the new value for each pixel by multiplying ... 1answer 31 views ### Inverse Laplace Transform A system given by$\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 ... 1answer 29 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. 0answers 23 views ### 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 ... 1answer 67 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 ... 1answer 34 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 ... 1answer 100 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 ... 1answer 53 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 ... 2answers 49 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 ... 2answers 144 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 ... 1answer 1k 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 ... 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$t=0$: $$F(j\... 0answers 15 views ### What is difference between natural response and zero-input response of a system and how to find natural response? [duplicate] In most books it is said that natural response is another name to zero-input response while in some resources is is mentioned that the classification is based on poles of transfer function and input.... 1answer 246 views ### Output of an LTI system given its transfer function and input Given the transfer function$$T(s) = \frac{100}{1 + \frac{s}{10^{6}}}$$and the input$$v_i(t) = 0.1 \sin(100t)$$find the output, v_o(t). My approach was to use v_o(t) = \mathcal{L^{-1}}\left\{T(... 0answers 43 views ### Region of convergence of transfer function I posted this question Mathematics SE and got no answer so I have posted it here. I learned in my signal processing class that an LTI system can be defined using a linear constant coefficient ... 1answer 32 views ### Time Setting of z and Laplace Transforms I'm aware that the z-transform and the Laplace Transform have an analogous relationship but I want to be doubly-sure that the z-transform only works in discrete-time and that the Laplace transform ... 1answer 49 views ### Why is the ROC of Laplace transform independent of imaginary part of s? An integral is defined as converging if it yields a finite value upon application of limits of integration. It is divergent otherwise. Now sticking to the mathematical notation of Laplace transform, ... 0answers 47 views ### Is there an analogy of the Fourier-decomposition in the Laplace space to decompose a signal to a few components? I have a signal from which I know, that it is the sum of a few, exponentially decaying components. I want to find these components. If it would be a sum of some sinusiod waves, it would be easy to ... 1answer 129 views ### How do bode plots work with unstable systems work? If I had a system with right-half s-plane poles, how would a frequency response work? Since a purely imaginary value for s, would cause the Laplace transform to diverge for such a system, what meaning ... 2answers 33 views ### System Response Terminology If I have a system specified by$$P(D)y(t)=Q(D)x(t)$$and I specify initial conditions y(0^-)=a, \ y'(0^-)=b,\ x(0^-)=c does the term x(0^-)=c correspond to the zero state response or zero ... 2answers 138 views ### Confusion Regarding Bi Linear Transform I was reading my book where the z-transform of a signal is derived to be {1-e^{-2bT}z^{-1}} . Then it goes on to say that by applying the bilinear transform we can get$$\frac{2(1+bT+(bT-1)z^{-1})}... 0answers 15 views ### 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$... 1answer 291 views ### Inverse Laplace transform of two-sided and one-sided Laplace transform As I read in Wikipedia, there are two types of Laplace transforms One-sided Laplace transform:$F(s) = \int_{0}^\infty e^{-st} f(t) dt$Two-sided Laplace transform:$F(s) = \int_{-\infty}^\infty e^{-...
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 ...
### 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 ...