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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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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Transfer function h(t) of a positive feedback system
I want to find the transfer function h(t) of the below positive feedback system. I came out till this.
How can i get the inverse laplace of this function? say β = 1 and γ = 1.
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Converting Laplace to CTFT to find solution
Let us take a system where the input is \$V_{i}(t)\$ and output is \$V_{o}(t)\$ and the impulse response of the system be \$I(t)\$ where \$t\$ represents time domain and \$w\$ be frequency. we get \$\...
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Dispersive delay line output and convolution is same or not?
I am trying to simulate chirp radar receiver with SAW filter (DDL) used in it. I struggle with formula for DDL output. I couldn't find it anywhere. As far as I understand convolution is flipping and ...
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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) \$: -
$$\begin{smallmatrix}\begin{array}{r|cc}
\text{Input} & \text{Output} & \text{...
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How do I find the impulse response of the system given output and input signals?
I stumbled upon this question as I was solving my homework.
There is an input signal x(t).
and y(t) as an output signal.
My idea was to find the function of y(t) in terms of step function and then ...
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What is the convolution of an antipodal (that is alternating 1 and 0) pulse train with rectangular pulse of duration T in the time domain?
What is the convolution of an antipodal (that is alternating 1 and -1) pulse train with a rectangular pulse of duration T in the time domain? I am having trouble picturing this.
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Convolution of positive and negative functions?
I am trying to do convolution for the function below
The correct solution is as follows:
I tried solving the problem, below is my attempt:
Can you please advise me where is my mistake?
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How to handle delta function after finding the impulse response?
I am pretending that laplace does not exist because I am being tested on these concepts separately.
Essentially, I have solved for the step response of a first order circuit and found it to be:
$$v_{c}...
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Find the Impulse response given input and output signals
I would like to know the technique to solve for impulse response given input and output signals.
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Help needed using convolution to calculate a system's impulse response
I have a circuit with the transfer function \$G(s) = \frac{1}{(s+1)^2}\$ and I'm asked to calculate the impulse response of the circuit. After looking into it I know that I need to use convolution ...
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Charge through a time-varying capacitor
If a capacitor has a time-varying capacitance, such that C(t) = C_0 + Kt, where K>0 is a constant. Then is charge-voltage relation, Q(t) = C(t)V(t) = (C_0 + Kt)V(t), valid? It should be noted that ...
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(Convolution Integral): What does it mean to have an impulse response before t=0?
Context: I am currently learning about convolution integrals as they apply to circuits (LTI specifically, if I understand it correctly.
(For the following, continue under the assumption that \$\theta(...
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convolution vs correlation?
Apparently this question looks better for DSP SE but I am posting it here to get answer in simple words for those EE graduates who didn't studied signal processing in undergrad.
Apparently as far as ...
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How to do convolution related problems? [duplicate]
I do not understand the concept of convolution. If possible could you please explain in layman terms so that I can solve this question.
What is the h(t)?
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General question about convolution and Fourier
I'm working on a system that includes a bunch of elements and I arrived at the following general expression for the output:
$$\mathcal{F}\left\{ T\cdot\left(\left[T\cdot\mathcal{F}\left\{ E_{1}\right\...
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Convolution integral with step function
for the following convolution integral
$$ \int_{-\infty }^{\infty}\sigma (\tau)\tau A\sigma(t-\tau)\sin(t-\tau)d\tau \text,$$ where \$\sigma(t)\$ denotes the step function
We'll only get results ...
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Why convolution in time domain is multiplication in frequency domain? [closed]
I am trying to understand intuitively why convolution is multiplication in frequency domain. I started at the mathematical derivation of this, but didn't understand what is happening intuitively. This ...
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Forward path gain
Consider a simple circuit consisting of a pair of wires, where input voltage is equal to output voltage.
Here forward path gain is G(s) = 1 ,(fig.1) which gives g(t) = δ(t) {Inverse Laplace ...
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Replacing s with jw in transfer function when the input function is oscillatory and has exponential decay
I understand a version of this question has been asked numerous times before but I could not find an answer to this specific one.
This is how I understood replacing s with jw. From the impulse ...
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The term Feed-forward and its meaning?
I am trying to understand the technical meaning of the term 'feed-forward', when and where it can be used and where it cannot be used? I have seen this term in various different areas.
For example:
...
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Change of variable from t to \$\tau\$ during convolution
I am not able to understand that in the standard convolution formula how we can change the variable from t to \$\tau\$.
$$\int{x(\tau)\cdot h(t-\tau)d\tau }$$
Isn't this incorrect mathematically?
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What is the time axis array after we convolve two functions in Matlab after sampling it with frequency \$f_s\$?
Suppose we have a continuous time function \$f(t)\$ , we sample it at frequency \$f_s, (t = -5:1/f_s:5)\$, and store it in an array \$a\$ in Matlab. Now we convolve it with itself using \$b = conv(a,a)...
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Contradiction while using the convolution sum for a non-LTI system
In a recent quiz, we were given the following problem:
The cascaded LTI systems \$\mathcal{T}_1\$ and \$\mathcal{T}_2\$ respectively have impulse responses \$h_1 \lbrack n \rbrack = \delta\lbrack n ...
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Determine the impulse response of the following discrete system
I'm not sure how they got the answer (provided below) for the following discrete system
y[n] = x[n]- 2x[n-2]+ x[n-3]- 3x[n-4]
the answer is given as .... h[n] = [1 0 -2 1 -3]
why is this? any help ...
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Brute-force convolution reverb in FPGA
I'm completely new to the world of FPGAs, and would like to get a sense of what is possible to achieve, and since I happen to have an interest in convolution reverb algorithms, I will use that example....
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How to construct a LTI system with a specific impulse response function, say \$h(t) = \delta '(t)\$?
I want to ask the question on a generic basis, but using \$h(t) = \delta '(t)\$ as my example.
I have Mathematical knowledge on the LTI system, but no hands on experience. In real life, how can we ...
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Define LTI system from a single input output pair
I am currently studying signals and systems, and am learning about LTI systems right now. I know any LTI system whose impulse response is known can be completely defined through the use of the ...
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What is the transfer function of an ideal buffer in time domain?
Convolution is is defined as the integral of the product of the two functions after one is reversed and shifted. And in a system where its transfer function is g and the input is f, the output is the ...
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2D convolution on 32x32 grayscale image on FPGA using verilog for inference of CNN
I am new to the world of convolutional neural networks and would like to implement a 2D convolution operation using the sliding window approach on a xilinx FPGA. The input to the image is a 32x32 ...
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Square wave autocorrelation integral
Given the following square wave signal g(t) :
I'm trying to find the \$R(\tau)\$ of this signal, but I'm confused about how to solve the integral.
In the signal above, the red square wave is the ...
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convolution of \$ e^{-t} \$ and 1-t
I cannot solve the convolution based on \$h= e^{-t}\$ for \$ t\ge0 \$ and \$u(t) = 1-t \$ when \$ 0 \le t \le1 \$.
Every time I try I keep getting a factor with \$ te^{-t} \$ whilst the answer shows:
...
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Convolution with two unbounded signals
So I have a convolution problem. I have two signals:
I need to find the output, y(t), through graphical convolution.
So I set the convolution integral up like this:
$$
\int h(\tau)*x(t-\tau)d\tau
$$...
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Fourier Transform - convolution theorem
I have been studying the Fourier Transform and the convolution theorem is not clear to me.
Sometimes, I see this:
But other times I see this:
Which one is correct? Where is this constant factor ...
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Multiplication and convolution
We know that squaring a signal doubles its bandwidth.
Can you please justify this case in time domain for non sinusoid signals,say Rect(t/T)? On squaring the signal i don't see any changes in tine ...
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Convolution integral for LTI system
We know that any continuous time signal can be expressed as follows:
$$x(t)=\int_{-\infty}^\infty x(τ)δ(t-τ)dτ$$
I came across a certain relation regarding linear time invariant systems . Using $$x(t)...
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Graphical CT Convolution
The question asks to compute the convolution of x(t) and h(t). While I know how to do this mathematically, using a combination of derivatives and integrals, I don't know how to convolve the two using ...
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How to find the Nyquist rate
I have the following signals and their Fourier transforms: \$x(t)\$ and \$r(t)\$. The signals are limited such that \$X(e^{j\omega}) = 0\$ for \$|\omega| > \Omega\$ and \$R(e^{j\omega}) = 0\$ for \$...
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Problem about the properties of convolution
I have a difficulty to understand the convolution integral itself. Can anyone please explain what are the differences between the following 3 convolutions?
x(t)*h(t), x(-t)*h(t), x(-t)*h(-t).
Thanks....
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Derivation of convolution integral from the discrete convolution sum?
I was wondering if anyone can provide a derivation of the continuous-time convolution integral
$$y(t)=\int_{-\infty}^{\infty}x(\tau)h(t-\tau)d\tau$$
from the discrete-time convolution sum
$$y[n]=\sum_{...
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Invertiblity of LTI System
Can any one please explain me how the convolution of the following leads to delta(t).
To convolve these to function i considered delta(t+T) as x(t) and
delta(t-T) as the response. Then these two ...
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Analog circuit for multiplying in the frequency domain [duplicate]
I have an idea I want to experiment with - doing boolean logic with analog (OFDM) signals. Each frequency component represents a different 'bit'. A key factor is performing the AND operation. I would ...
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Concept of convolution
I am having trouble understanding the concept of convolution. I get the mathematical idea behind it. I am able to evaluate that the convolution of the following problem
is $$f*g(t) = {0,\ \ t <= -...
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How to derive the solutions of the Differential Equations when using convolution?
I am currently learning convolution (which is not the easiest topic for sure). Just as by many fields in electronics also here are differential equations involved. With this (what I have seen until ...
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Finding Filtered Output using Convolution property of Continuous Fourier Transform
why the derivative of u[t] is delta[t] ?
also I don't understand why the sin term disappeared once the derivative is taken.
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Effect on signal bandwidth due to multiplication?
Recently I came across an statement which says,
If signal m(t) has bandwidth B then pow(m(t),n) will have bandwith nB.
To prove it mathematically I startted with,
Let n=2,
y(t)= m(t)xm(t)
y(t)=...
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