Questions tagged [convolution]
Anything related to convolution, its properties and applications. Convolution is the mathematical operation which is used to model the time-domain I/O relationship of linear time-invariant initially-at-rest systems.
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How to find the Inverse Laplace Transform of \$\frac{1}{(s^2+1)^2}\$ or \$\frac{s^2}{(s^2+1)^2}\$ by PFE?
From the Laplace transform table formula 11 and 12, we have \$\mathcal{L^{-1}}\{\frac{s^2}{(s^2+1)^2}\} =\frac{1}{2}(sin t + tcos t)\$ and \$\mathcal{L^{-1}}\{\frac{1}{(s^2+1)^2}\} =\frac{1}{2}(sin t -...
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Finding overlap area when using graphical method for convolution of signals
I am given 2 rectangular functions where x(t) is flipped and shifted over h(t). Red is x(t) and blue is h(t).
When t is between 4 and 6 (i.e. 4 < t <= 6), why does the overlap (i.e. output y(t)) ...
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Convolution with scalar value
What would be the convolution of u(t) with (-1+2u(t))?mainly what I want to know is how the scalar part should be dealt in convolution?
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Convolution of unit step function with the mirror image of unit step function
What will be the convolution of u(t) with u(-t) using convolution integral? I am confused about the limits of the integration.
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Unilateral laplace transform of rect(t/2)
What would be the unilateral laplace transform of rect(t/2)? We know that rect(t/2) can be written as u(t+1)-u(t-1).So what would be its unilateral laplace transform?
Should it be (exp(s)/s)-(exp(-s)/...
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Integration of signal [closed]
How can I solve this integral? I know this integral is equivalent to convolution with u(t). Hence the convolution of u(t) with u(t) is r(t) or ramp function. But what would be the convolution of u(...
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How can I solve this (convolution) integral? [closed]
Let \$x(t) = \sigma(t)\$ where \$\sigma(t)\$ is the unit step function, and
\$h(t) = e^{-4t} \cdot \sigma(t)\$. When I try to solve the convolution \$x(t) \ast h(t)\$, I get
$$ x(t) \ast h(t) = \...
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Implement a 5 Layered CNN for inference on Arduino
I'm working on a problem where we convert a 5 layered CNN which is capable of predicting the possibility of an epilepsy episode (yes or no), into a Spiking Neural Network (SNN), making it useful for ...
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Inverse Laplace transform not giving correct result
How does one calculate the inverse Laplace transform of \$V(s) = \frac{1}{(s+α)(s+β)} \$? Laplace transform of function $$V(t) = \frac{1}{β-α}(e^{-αt} - e^{-βt})$$ is $$V(s) = \frac{1}{(s+α)(s+β)}$$...
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Missing mathematical step in convolution sum [closed]
I am looking at an example on convolution sums. In the example it states the following:
$$ \sum_{k=-\infty }^{n }2^{k} = \sum_{m=0}^{\infty }\left(\frac{1}{2}\right)^{m-n} $$
I feel I am missing some ...
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How to convolve these two signals?
I tried to convolve these two signals (top image). I’m not sure if I have done it properly. My partial answer (further below) is wrong.
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Convolution sum of discrete signals
This is a problem from Michael Lindeburg's FE prep book - find the convolution sum v[n] = x[n] * y[n]. I am familiar with the graphical method of convolution. However, I am not familiar with ...
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Derivation of zero state response for LTI system with convolution
Consider this derivation of the zero-state response \$y_{zs} \$ for an LTI system caused by an input \$x(t) \$: -
$$\begin{smallmatrix}\begin{array}{r|cc}
\text{Input} & \text{Output} & \text{...
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How do I find the impulse response of the system given output and input signals?
I stumbled upon this question as I was solving my homework.
There is an input signal x(t).
and y(t) as an output signal.
My idea was to find the function of y(t) in terms of step function and then ...
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What is the convolution of an antipodal (that is alternating 1 and 0) pulse train with rectangular pulse of duration T in the time domain?
What is the convolution of an antipodal (that is alternating 1 and -1) pulse train with a rectangular pulse of duration T in the time domain? I am having trouble picturing this.
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