# Questions tagged [laplace-transform]

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### Finding the system output by convolution

pretty new to this concept, so do bear with me. A linear dynamic system is described by the following differential equation: Transfer function H(s) is calculated to be = I've already found the ...
92 views

### 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 ...
30 views

### How can I find the transform function, amplitude and frequency response of a digital filter in python?

I have applied a laplace filter mask to an image and now I want to find the amplitude and freqency response of a laplacian filter: [[1,1,1], [1,-8,1], [1,1,1] ]. I know I need to first find the ...
58 views

### 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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### 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 ...
33 views

### Validity of applying Heaviside function for signal processing applications

I wasn't sure if this question was more suitable for math.stackexchange, but I suspect it's more-so a signal processing question (albeit, a theoretical one) than a mathematical one. I am currently ...
533 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 ...
102 views

### How can I plot the frequency response on a bode diagram with Fast Fourier Transform?

Assume that we have an unknow dynamical system and we only want to estimate its parameters. The system can be discribed as: Continous time: $$G(s) = \frac{3s + 5} {5s^2 + 3s + 2}$$ Discrete time ...
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### How Can I Add noise to a Frequency Domain Input Signal?

I am new with Matlab and doing some work on Amplifier and Bipolar Shappers Amplifiers. Adding Noise to a Time Domain Signal is quite easy and I have done it multiple time as: ...
166 views

### Why does the unit step function not have infinite poles?

Let's say I have a transfer function which is a unit step function. $H(s) = \int_{0}^{∞}e^{-st}dt$ But when we write, $H(s) = 1/s$ it is only true when $Re(s) > 0$ So after we derive the ...
260 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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### How to compute Laplace Transform in Python?

I am trying to do practicals for signal processing where I need to Laplace Transform a function. Used 'fft' of numpy before. Nothing of Laplace is found in the documentation. Do we have any other ...
5k views

### Why is a negative exponent present in Fourier and Laplace transform?

could anyone explain why there is a need of negative exponent in fourier and laplace transform.I looked through the web but I couldn't get anything.Does anything happen if a positive exponent is ...
1k views

### Is the Laplace transform a special case of Fourier transform? (Not the other way around)

Always had a thought about why Laplace transform reveals the transient properties of the system? My doubt is based on the following fact, Fourier transform is given as  \begin{equation} \mathscr{F}\...
451 views

### When to use Fourier, Laplace and Z transforms?

If we have an LTI system, with an input signal $x(t)$, impulse response $h(t)$ and output $y(t)$, I was under the assumption that if the input and impulse response were continuous in time, then you ...
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### What are the properties of continuous-time improper systems?

I am trying to better understand the properties of improper systems $H(s) = \frac{b(s)}{a(s)}$, for which the order of the numerator $b(s)$ is greater than the order of the denominator $a(s)$ (in the ...
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### Recovering a Differential Equation From the Transfer Function of a Cascaded System

With respect to the below discussion, consider that we are talking about LTIC systems characterized by constant coefficient ODEs. Consider a cascaded system whose transfer function H(s) is given by ...
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### How to derive low pass filter $\frac{N}{N+S}$

I watched the video for PID control system where it mentioned the Laplace domain function and low pass filter to be $\frac{N}{N+S}$. I used asymptotic analysis to see that it made sense. However, I'm ...
453 views

### Transfer function of a frequency shifting system

There is a system which shifts frequencies of input by $-F_c$ such that: $$Y(S) = X(S).H(S)$$ But $X(S)$ has value zero from $0$ to $F_c$. I am confused on how the product of $X(S)$ and $H(S)$ ...
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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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### Relation between Laplace and Fourier transforms

I know that $$X_L(s=j\omega)=X_F(\omega)$$ if $x(t)$ is one sided and absolutely integrable and hence the imaginary axis of the Laplace transform is the Fourier transform. But Fourier transform ...
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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 ...
3k views

### What's the meaning of a complex zero/pole?

I have been studying signal processing and control for a while now, and I use Laplace and Fourier transforms almost everyday. Also another tools such as Nyquist or Bode plots. However, I had never ...
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### Determine the system function H(s) of a system and find out the differential equation

I have created the following system for practice purposes. From this system I want to determine the system function H(s). In the picture I have worked with auxiliary (dummy) variables, which should ...
65 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. ...
71 views

### 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 ...
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### 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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### 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 ...
86 views

### 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 $y0=0$ $F(s) = m * s^2 * y(s)$ $y(s) = F(s)/(... 1answer 40 views ### How to know basics about convergence I apologize if the post is incorrect. I'm a sophomore student studying Electrical engineering. As a part of an introductory course on signal and linear systems, I'm required to learn Fourier and ... 0answers 25 views ### What are the missing steps in the derivation of this equation? I am trying to understand the model of a piano hammer described here. The relevant excerpt is: As I understand it, they are saying in (12a) that if the hammer spring's uncompressed end's y position ... 1answer 61 views ### s-Domin or z-Domain - What to Use for Mixed systems I recently had to deal with a power electronic system where I had to implement a dynamic model of a power converter in order to design a suitable controller for that converter. The control will be ... 2answers 352 views ### Help with my first (simple) Z-transform I need to transform this Laplace function to the z-domain: From the answer I received:$s=(1-z^{−1})/T$Then substitution into my Laplace function would give:$t(z) = 2R/(m*(1-z^{−1})/T + 2R)$Is ... 1answer 366 views ### Why the unilateral Laplace transform? Why is the Laplace transform commonly taught as the unilateral Laplace transform? I mean, for the Fourier transform, we commonly have the bilateral transform... if the signal is 0 for$t<0$, then ... 0answers 24 views ### Solving the system response using inverse Laplace transform I am trying to solve this question but I got stuck when inverting the Laplace transform for this problem. I do not know that whether I do it right or wrong. Moreover, I do not know how to handle the ... 1answer 44 views ### Determining Stability of a continuous time system using Laplace Transform I'm following Oppenheim's book. In exapmles, the laplace transforms of of the following signals$e^{-t}u(t)$and$e^{-t-1}u(t+1)$is given as$\frac{s}{(s+1)}$and$\frac{e^{-s}}{(s+1)}$both ... 2answers 88 views ### Why Are There Two Different Common$ 3 \times 3 $Kernels for the Laplacian? I find both of these 3x3 Laplacian kernels to be commonly used: 0 -1 0 -1 4 -1 0 -1 0 and: -1 -1 -1 -1 8 -1 -1 -1 -1 ... 2answers 3k views ### blur detection using opencv I'm writing a script to detect blur images using OpenCV by applying Laplacian filter and calculate the std but there is a problem the std for images that contain motion blur is very close to those ... 3answers 27k views ### How poles are related to frequency response I have recently fallen into fallacy, considering pole s=1 as there is infinite response at frequency 1. Yet, response was only 1. Now, can you derive the frequency response, given the poles? ... 3answers 300 views ### Why do convolution kernels such as Gaussian, Laplacian, LoG almost always seem to be expressed in integers? I'm a total newb in search of some deeper understanding, but I'm not able to read the maths behind these on Wikipedia. If I understand correctly, you get the new value for each pixel by multiplying ... 1answer 48 views ### Inverse Laplace Transform A system given by$\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 42 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 25 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 99 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 64 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 ...
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 ...