Questions tagged [laplace-transform]

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2 votes
4 answers
15k views

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 ...
1 vote
1 answer
63 views

Laplace transform of derivative

Here is a short proof that Laplace Transform of $x'(t)$ is Laplace transform of $x(t)$ multiplied by s: On the other hand, the proof that I know uses integration by parts: One condition for the ...
1 vote
2 answers
96 views

Transfer function and Laplace domain

If we give a input $x(t)=u(t)$ to a system $\mathcal{S}$ we get an output $y(t) = e^{-t} u(t)$. After we Laplace-transform both the input and the output we get the transfer function $$H(s) = 1-\frac{1}...
3 votes
1 answer
45 views

Name of property of Laplace transform

\begin{align} L[e^{-at}u(t)] &= \frac{1}{s+a}\\ L[\cos(\omega_{o}t)u(t)] &= \frac{s}{s^{2}+\omega^{2}_{o}}\\ L[e^{-at}\cos(\omega_{o}t)u(t)] &= \frac{s+a}{(s+a)^{2}+\omega_{o}^2} \end{...
0 votes
0 answers
28 views

Amplitude ratio is larger than 0.5 on a RC-filter if RC = 1.7684e-03

I have two signals ...
0 votes
0 answers
26 views

Confusion understanding expression (greater than /less than sign) Region of convergence in s domain?

I'm having trouble understanding the highlighted line $\text{Re}(s) > -a$ in the attached snapshot. What does that mean? Will our Region of convergence will be towards the right of $a$ or towards ...
0 votes
2 answers
157 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 $y(0)=1$...
1 vote
1 answer
39 views

Sampling with impulse train

There are many times when the textbooks used by all university students like me make an introduction to the notion of sampling of a continuous-time signal with an impulse train as shown below. Why do ...
1 vote
1 answer
60 views

Prove that the filter is stable, causal and minimum phase

I have a system which has the following transfer function $$H(s)=\frac{\beta + s}{s^{2} + 2\alpha s + \beta^{2}}$$ where $\beta = \sqrt{\omega^{2} + \alpha^{2}}$ and $\alpha>0$. This system, as ...
4 votes
2 answers
72 views

Study the stability of $H(s)=\frac{\beta + s}{s^{2} + 2\alpha s + \beta^{2}}$

I have a system which has the following transfer function $$H(s)=\frac{\beta + s}{s^{2} + 2\alpha s + \beta^{2}}$$ where $\beta = \sqrt{\omega^{2} + \alpha^{2}}$ and $\alpha>0$. The degree of ...
2 votes
1 answer
105 views

What is the Laplace Transform of the output power spectrum if the input signal is a white noise?

Let us consider a random wide-sense stationary process $n(t)$, which passes through a filter $h(t, \tau)$. Its autocorrelation function is $$R_{n^\prime}(t)=\int_{-\infty}^{\infty} \int_{-\infty}^{\...
-1 votes
2 answers
84 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 ...
2 votes
1 answer
49 views

making a laplace s-domain plot from numerical data to decompose signal into decaying sinusoids

I would like to make a 3D laplace s-domain plot from experimental data I have. The examples I have seen for this are when the function is already known and an analytical solution can be obtained (...
5 votes
1 answer
339 views

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 ...
0 votes
1 answer
23 views

Reference for Wiener-Kolmogorov whitening procedure

In an old paper, accessible only for a fee, I found: (where the LHS of Eq (5) lack the symbol of derivative). What is the Wiener-Kolmogorov whitening procedure? I would like to study this procedure, ...
2 votes
1 answer
40 views

How does the phase/gain margin method work?

We have the closed loop transfer function: $$T(s)=\frac{L(s)}{1+L(s)}$$ So as far as I understand we check along the $j\omega$-axis on the Bode plot whether $L(s)=-1$, cause that's when $T(s)$ has ...
0 votes
1 answer
40 views

Time invariance in transfer functions

I read this in a book: here ${\cal L}[x(t-a)u(t-a)]$ is the laplace transform of a time shifted function $x(t)$ shifted by $a$ seconds and we know that transfer functions have the formula $H(s)=Y(s)/...
4 votes
1 answer
101 views

Finding and displaying Laplace or Z transform ROC(region of convergence) using MATLAB

Is there any way, we can use MATLAB for finding and displaying Laplace or Z transform Region of convergence?
2 votes
1 answer
67 views

Confusion regarding Laplace transform calculation in MATLAB

I am trying to learn about Laplace transform and especially about ROC and i found out on this weblink. I have also attached a snapshot of this link and highlighted where it is being said that although ...
1 vote
1 answer
167 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 $$0.9 (z^2 -1.14z + 0.941)$$ and $$z^2 - 1.0232z + 0.757$$ Does anyone explain how he got those numbers?
0 votes
1 answer
1k 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 ...
1 vote
1 answer
647 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 ...
-1 votes
1 answer
124 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 ...
0 votes
1 answer
50 views

Bandwidth of a given function

Suppose the signal given is $x(t)=(cos(5t)+e^{-2t})u(t)$ and the goal is to find the bandwidth of this signal. We know the bandwidth, $B$, is just $f_{max}-f_{min}$. Our first step is taking the ...
4 votes
1 answer
585 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 ...
1 vote
1 answer
88 views

Find $A$ and $G$ value to satisfy the requirement

Given a disturbance reduction system Create a system that will reduce $U(s)$ noise to $100$ times its value. Find the A and G gain value to satisfy the requirement My attempt: I've analyzed the ...
4 votes
2 answers
419 views

Product of Doublet and Arbitrary Function

We know that the product of the delta function and another function samples the latter function. That is, $$ \delta(t-\tau)f(t)=\delta(t-\tau)f(\tau) $$ Does the doublet function retain this same ...
1 vote
1 answer
236 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 ...
0 votes
0 answers
21 views

Step response of a given input and output (Laplace or Fourier)

I am trying to calculate the step response of the following given: Should I use Laplace transform or Fourier transform?
3 votes
2 answers
412 views

How do I convert this simple Laplace equation to Z-domain?

A basic model of coupled strings (eg. piano) is provided in DSP Related - JULIUS O. SMITH III - PHYSICAL AUDIO SIGNAL PROCESSING - FOR VIRTUAL MUSICAL INSTRUMENTS AND AUDIO EFFECTS- Two Coupled ...
2 votes
3 answers
147 views

Are there any examples of "Causal" Continuous-Time Linear-Time-Invariant Systems (CT-LTI) with output given by finite-duration functions?

Are there any examples of "Causal" Continuous-Time Linear-Time-Invariant Systems (CT-LTI) with output given by finite-duration functions $y(t)$?? With output I am meaning that $y(t)$ is such ...
1 vote
0 answers
99 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 ...
1 vote
2 answers
51 views

Filter filters out more than needed

I am currently coding a school assignment. I have a 1.5s recording of someone's speech that has 4 rogue cosines mixed in. With sampling rate 16000Hz, I divided the recording into frames of 1024 ...
0 votes
1 answer
65 views

The Laplace transform - Steven W. Smith Book - impulse response cancellation method

While studying the Laplace transform using Steven W. Smith Book I found something uncomprehending. In the 32th chapter - The Laplace Transform, page 590, last paragraph describes the cancelling ...
1 vote
2 answers
453 views

Confusions regarding differences between Fourier transform & Laplace transform?

Although this topic has already been addressed in multiple popular questions of SE but i have few confusions in this regard Number 1) Link of question https://electronics.stackexchange.com/questions/...
0 votes
1 answer
55 views

What will the output of a system which has no Fourier transform?

Let's assume a system $h(t)= e^{j2t}$. This system has no region of convergence. What will be the output if I provide any input to this system?
10 votes
2 answers
2k views

What is the difference between $X(j\omega)$ and $X(\omega)$ notation?

What is the difference between $X(j\omega)$ and $X(\omega)$ notation? What is the meaning of $j\omega$? Does it represent frequency, and if yes, what is the meaning of an imaginary frequency?
5 votes
1 answer
10k 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 ...
1 vote
2 answers
454 views

How are pole-zero plots, magnitude response plots, and phase response plots related?

Given that the Laplace transform of a continuous-time signal $h(t)$ is $H(s)$, what can a plot of the poles and zeros of $H(s)$ on the $s$-plane tell me about the magnitude response and phase response ...
0 votes
3 answers
279 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 ...
5 votes
1 answer
225 views

Connection from Fourier to Laplace Transform

I have a basic understanding of Laplace and Fourier but having trouble making a connection. Every time I attempt to look at reasons these are connected I'm told about the s-plane and regions of ...
0 votes
0 answers
17 views

Optimal FWHM for Difference of Gaussians edge detection

When we apply a Gaussian blur to a a dataset, we set the FWHM to optimally detect specific frequencies. For example, the human cortex is around 2.5mm thick, so a blur with 2.5mm FWHM is nicely tuned ...
0 votes
2 answers
299 views

Laplace transform of averaging operator

I am studying dc-dc converter now. I got a problem with Laplace transform of the averaging operator as in the image below. Can anyone help me derive the Laplace transform result $G_{av}(s)$ as in the ...
1 vote
1 answer
284 views

Can we tell if a system is linear and time-invariant from its frequency response?

Given a system with a known frequency response in the S-domain. Is there a way to find whether the system is linear and time invariant? My current understanding is that we need to take the inverse ...
1 vote
1 answer
404 views

How to get state-space equations form from a block diagram?

This is the block diagram that I'd like to transform into a state-space representation, where u1 and u2 are inputs and y1 and y2 are the outputs of the system I tried to place state variables on the ...
1 vote
1 answer
43 views

Mixed - Discrete and Continuous system Laplace domain stability - Effect of Sampler and DAC

I have a system whose the plant transfer function is continuous and the compensation is discrete. I have an ADC which allows to measure the output of the system and a DAC which allows to control the ...
1 vote
0 answers
54 views

Laplace transform plot isn't right

I'm trying to plot the Laplace transform of a function. Here's my MatLab script ...
1 vote
1 answer
39 views

Why RHP zero phase is not 180° to 90°

The asymptotic phase behavior of an RHP zero is from 0 degrees to -90°, the mirror of an LHP zero. Graphically, I'm confused about why this is the case and the phase is not from +180° to +90°. See the ...
0 votes
2 answers
887 views

A system having impulse response $ h(t)=u(t) $ stable or not?

I know that for a system to be BIBO stable its impulse response must be absolutely integrable and the impulse response $ h(t)= u(t)$ integrates to approach infinity (i guess) I proceeded as$$ \int_{-\...
2 votes
1 answer
86 views

Unilateral Laplace Transform's Differentiation Property

I've read in numerous places that the unilateral laplace transform is extermely useful in solving differential equations with initial conditions based on the differentiation property of the unilateral ...