# Questions tagged [laplace-transform]

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### 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, ...
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### 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 ...
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### 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 ...
368 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 ...
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### 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?
1 vote
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### 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 ...
60 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 ...
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### 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?
1 vote
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### 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/...
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### 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
323 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 ...
159 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 ...
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### 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 ...
1 vote
237 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
207 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
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### 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
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### 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 ...
1 vote
51 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