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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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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?
Abrar Fahim's user avatar
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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.
Abrar Fahim's user avatar
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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)/...
Abrar Fahim's user avatar
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1 answer
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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(...
Abrar Fahim's user avatar
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related to convolution drawing of signals and systems

I can draw the graph in unit digits, but I have no idea how to draw the function 3π(t-3/2) below it. I wonder how can we plot this?
softcalculate's user avatar
2 votes
1 answer
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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) = \...
emircg02's user avatar
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1 answer
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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 ...
satan 29's user avatar
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3 answers
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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 $$V(s) = \frac{1}{(s+α)(s+β)}$$...
Amit M's user avatar
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1 answer
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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 ...
Qubit's user avatar
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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.
Thomas Edison's user avatar
1 vote
1 answer
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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 ...
vasiqshair's user avatar
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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{...
Carl's user avatar
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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 ...
TeilZeitGott's user avatar
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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.
user4434's user avatar
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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?
OMAR's user avatar
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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}...
amateurhour's user avatar
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2 answers
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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.
TeilZeitGott's user avatar
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1 answer
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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 ...
MendelumS's user avatar
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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 ...
Vikash's user avatar
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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(...
SerasVita's user avatar
4 votes
3 answers
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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 ...
DSP_CS's user avatar
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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)?
Bboy Machu's user avatar
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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\...
FlyGuy's user avatar
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1 answer
375 views

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 ...
Pilotf4's user avatar
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1 answer
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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 ...
Omibuddyy's user avatar
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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 ...
Vasu Goyal's user avatar
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3 answers
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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 ...
Absolut's user avatar
7 votes
3 answers
1k views

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: ...
alt-rose's user avatar
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2 votes
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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?
Siddharth's user avatar
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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)...
helloworld1e.'s user avatar
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1 answer
108 views

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 ...
Pranshu Malik's user avatar
2 votes
1 answer
509 views

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 ...
wwjrmmr's user avatar
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2 answers
676 views

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....
Olivier Sohn's user avatar
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1 answer
66 views

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 ...
H42's user avatar
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2 answers
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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 ...
jan kowal's user avatar
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1 answer
305 views

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 ...
pnatk's user avatar
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1 vote
1 answer
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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 ...
frisco_1989's user avatar
4 votes
1 answer
3k views

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 ...
Yannick's user avatar
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2 answers
1k views

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: ...
Weird's user avatar
  • 15
2 votes
1 answer
470 views

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: $$ \int h(\tau)*x(t-\tau)d\tau $$...
Adam's user avatar
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1 vote
1 answer
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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 ...
Vinícius Lopes Simões's user avatar
1 vote
1 answer
673 views

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 ...
ritvik rathore's user avatar
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2 answers
341 views

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)...
John Katsantas's user avatar
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2 answers
4k views

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 ...
Wei's user avatar
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1 answer
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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 \$...
user avatar
0 votes
1 answer
154 views

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....
Canberk's user avatar
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1 answer
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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_{...
Ben Granger's user avatar
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2 answers
42 views

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 ...
Mayank Pal's user avatar
2 votes
2 answers
407 views

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 ...
DeusXMachina's user avatar
2 votes
3 answers
2k views

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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