Questions tagged [laplace-transform]

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Part 2: Root Locus, Transfer Functions and Unit Step Response?

I'm continuing my question referenced here: Part 1 Question / Problem Description Say I have a new Root Locus shown below Consider the generic feedback loop, and the transfer function $G(s)$ shown by ...
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29 views

Root Locus, Transfer Functions and Unit Step Response?

Consider the generic feedback loop, and the transfer function $G(s)$ shown by the following root locus plot. Where $\mathbf{x}$ denotes the open-loop poles and $\square$ denotes the closed loop poles....
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transfer function of a sampler in the s domain

I would like to modelize my whole system into the S-domain. This is a mixed system, there a numerical part (corrector, ADC, DAC) and an analogic part (plant transfer function, sensors, etc...). I know ...
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57 views

How to calculate critical damping of a system with two springs and a damper (or two springs and two dampers)?

Background For a simple system where you have a mass attached to a spring and damper in parallel: We can calculate the critical damping from the equation of motion: $mx_{tt} + cx_t + kx = 0$ $ms^2 + ...
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How to solve this Laplace integral for an averaging function in an iterative numerical (finite difference) model?

I am trying to implement a mathematical model for vibrational damping described in this article. They provide an equation for damping force ($F$) as a function of: a spring constant ($k$) a damping ...
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74 views

Why not use the same “standard” exponentials for both continuous and discrete time

In continuous time the standard exponential signal is usually defined as $$ e^{st}, \quad\text{with}\quad s = \sigma+j \omega $$ In discrete time the standard exponential signal is usually defined as ...
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41 views

If the impulse response of a causal LTIC system is $h(t) = \delta(t) + \sin(t)u(t)$, is it marginally stable or unstable (BIBO)?

If you take the $H(s) = \mathcal{L}[h(t)]$ the poles are on the imaginary axis so the system should be marginally stable, but is it?
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41 views

Confusion for two-sided signal

Given a continuous LTI system with transfer function $$H(s)= -\frac{2s}{(s+6)(s+2)}$$ Plot the location of the pole(s) and zero(s) Find all possible regions of convergence From the problem above find ...
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51 views

Why can you use the one-sided laplace transform to solve differential equation describing a causal LTI-system?

In an example, an equation describing a causal LTI-system is $$ (D^2 + 5D + 6) y(t) = (D+1) x(t) $$ where $y(t) = y_{zs}(t) + y_{zi}(t)$ and the initial conditions are $y(0^-) = 2, \dot{y}(0^-) = 1$. $...
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Laplace Transform: zeros and corresponding impulse response $h(t)$

Poles and the impulse response If our impulse response is in the form : $$h(t) = e^{-\sigma_0 t}\cos(\omega_0 t) \, u(t)$$ (where $u(t)$ is the unit step function) And its Laplace transform is : $$H(s)...
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24 views

RoC and Stability of a Rectangular Signal

If we have a system with an impulse defined as: $$h(t)=u(t)-u(t-2)$$ Then the Laplace Transform of h(t) would be the transfer function: $$H(s)=\frac{1}{s}-\frac{e^{-2s}}{s}, \quad Re(s)>0$$ We also ...
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58 views

Laplace transform : integral vs poles & zeros

If Laplace transform is expressed as : $$\int_{-\infty}^{+\infty} h(t)e^{-st}dt $$ with : $$s = \sigma + j\omega$$ and $h(t)$ an impulse response expressed as : $$h(t) = Ae^{-\sigma_0t}\cos(\omega_0t+\...
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49 views

Discrete time Final Value Theorem applied to feedback system

I wish to calculate the Final Value of systems in which a high pass filter of the output feeds back into the input. A simple example would be: where is a 1st order high pass filter with transfer ...
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Moving from deterministic signals to stochastic signals in s-domain (Power Spectral Density)

Assume we have the following system (coming from control systems theory, hence in s-domain) $ Y(s) = H_A (s) \cdot A(s) - H_B (s) \cdot B(s) $ I now wish to consider $a(t)$ and $b(t)$ as white noise ...
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63 views

Inverting a sampled system

I'm doing some self-study for an upcoming exam and came across the following question: My first idea to solve it was using the bilinear transform to get some approximation of $H(Z)$ (or just using ...
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67 views

Why is Fourier space not adequate for (theoretical or digital) filters?

As far as I have seen, almost all theoretical filter design occurs in Laplace or Z-space. Also, there is a pervasive connection to real life analog filters in the design. If one is just thinking in a ...
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How to I get transfer function?

there is a ODE $dx/dt-ax(t)=u(t)$ Firstly, I have to find the transfer function $u$ to $x$ using exponential input. So I put $u(t)=e^{st}$ to the ODE, and I got $x(t)=x(0)e^{at}+1/(s-a)e^{st}$. In ...
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Confusion in property of Z transform of ideal sampled waveform

I was reading about z transfom of ideal sampled signals and one of the properties of Z transform of sampled signal that surprised me,here it is (image) So here this property of Z transform is quite ...
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44 views

Real impulse response

It will be great if someone can explain me what exactly means "real impulse response". Further more , what is the effect of such a response on ROC (Laplace plane) and in particular if its ...
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75 views

Fourier Transform of an Exponential Sine Sweep

The Exponential Sine Sweep (ESS), according to Farina [1], can be described by the following formula: $$x(t)=\sin\left(\frac{2\pi f_1 T}{R}\left(e^{\frac{t R}{T}} -1\right) \right)$$ where, $t$ - ...
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76 views

Confusion in initial condition of differential equation using Laplace transform transform

I'm confused in solving linear constant coefficients differential equations (LCCDEs) by Laplace transform if initial conditions are given at time just before $t=0$ just after $t=0$ exactly at $t=0$ ...
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186 views

Impulse response if initial conditions are given

In most books, impulse response of LTI systems are calculated by assuming initial rest condition, but how to calculate response of an impulse input if there are some initial conditions present ? My ...
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142 views

How can I find the transfer function of the following block diagram?

I've the following image and I want to find the transfer function from input $x(t)$ to output $y(t)$. I know that I have to apply Laplace Transform, so the integrator becomes $\dfrac{1}{s}$, but I don'...
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How to compute transfer function $G(s) = \exp \left( - \sqrt{s} \right)$ in Matlab / Simulink?

How to compute transfer function $$G(s) = \exp \left( - \sqrt{s} \right)$$ in Matlab / Simulink? I am trying to calculate a PID controller for this function. This function describes heat transfer via ...
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1answer
36 views

Compute output given input, transfer function and initial conditions

The problem statement is Consider a causal LTI system whose transfer function $H(s)$ is given as $$H(s)=\frac{s+2}{(s+3)(s+4)}$$ Compute the output $y(t)$ for an input $x(t)=e^{-2t}u(t)$ when $y(0)=1$...
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28 views

Names of system functions in frequency domain

I was just trying to refresh my systems theory known from long ago, and I realized that I had forgetten the name of the basic functions. Specifically, what are the names of these functions ...
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31 views

Apply Transfer Function in Continuous Domain in Matlab

I have the coefficients of a transfer function (i.e. numerator and denominator) in Laplace domain. How can I apply this to an input waveform using MATLAB script? I am looking for a function or piece ...
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107 views

Fourier transform of unit step

I was reading pdf by caltech and in one of its section, Fourier transform of Unit step signal is calculated but I am confused, how this can be possible if region of convergence for Laplace transform ($...
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1answer
57 views

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 ...
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56 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 ...
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47 views

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: ...
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198 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 ...
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741 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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1answer
2k views

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 ...
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48 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 ...
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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}\...
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570 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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1answer
53 views

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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45 views

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 ...
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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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1answer
263 views

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 ...
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1answer
77 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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67 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 ...
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109 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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66 views

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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272 views

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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100 views

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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37 views

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 ...
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367 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 ...