Questions tagged [convolution]
Questions on the (continuous or discrete) convolution of two functions. It can also be used for questions about convolution of distributions (in the Schwartz's sense) or measures.
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Proving an integral identity: $\int\nolimits_{-\infty}^\infty x f(x)f(t-x) dx =\frac{t}{2} \int_{-\infty}^\infty f(x)f(t-x) dx $
Let $f$ be a nonnegative (probably not needed) function on $\mathbb{R}$ such that for all $t$, $xf(x)f(t-x)$ and $f(x)f(t-x)$ are both integrable in $x$.
Is it true that $$ \int\nolimits_{-\infty}^\...
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LTI: How to calculate the step response of this impulse response?
i need to evaluate the convolution sum of x[n] * h[n].
x[n] is the step function u[n].
I know how the output should look like but i don't know how i can calculate it.
I think the lower border is 0, ...
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How to sketch the following discrete time signal?
i need to sketch y[n] where * denotes the convolution operator and delta is the unit impulse.
I know how to sketch x[n-1] and delta[n-2] but i have problems with the convolution.
In my script i only ...
- 439
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Convolution of triangle function with itself
I'm trying to find the convolution $(A \ast A)(x)$, where
$$A(x) = \begin{cases}
1 + x, & -1\leq x \leq 0,\\
1 - x, & 0\leq x \leq 1,\\
0, & \text{otherwise},
\end{cases}$$
so far ...
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"anti-gaussian" 2D convolution kernel
What is the 2D kernel, k, that when convoluted with a 2D signal, f, that is convoluted again with a gaussian 2D kernel, g, produces a result that is closest to the original signal, f'.
Something like ...
user8086
6
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Convolution of compactly supported function with a locally integrable function is continuous?
Can someone show me the proof that the convolution of a compactly supported real valued function on $\mathbb{R}$ with a locally integrable function is also continuous? I feel that this is a standard ...
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Commutativity of convolutions implies $\int\limits_{-\infty}^\infty f(t)dt = \int\limits_{-\infty}^\infty f(t-a)dt$?
As I understand it, to convolve $f$ and $g$ means to find $\displaystyle \int_{\mathbb R} f(a)g(t-a)da$, which is also apparently commutative, and therefore $\displaystyle \int_{\mathbb R}f(a)g(t-a)da ...
user7634
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Preservation of Lipschitz Constant by Convolutions
The following is a step in a proof: $f$ is a Lipschitz function from $E$ to $F$ where $E$ is a finite-dimensional Banach space and $F$ an arbitrary Banach space. $\phi\geq 0$ is a $C^\infty$ function ...
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Limits and convolution
Let $f,g \in L^2(\mathbb{R^n})$, $\{ f_n \}, \{ g_m \} \subset C^\infty_0(\mathbb{R}^n)$ (infinitely differentiable functions with compact support) where $f_n \to f$ in $L^2$, and $g_n \to g$ in $L^2$....
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A convolution identity (revision of the question "Is this convolution identity known?")
I have deleted the content of the original post.
The following exercise is inspired by answers to the questions this and this, but no knowledge of probability theory is required. The solution is ...
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Convolution on group with measure
I was wondering about the generalization of the concept of convolution from the familiar one on real spaces and how many properties still remain.
For convolution on Lebesgue-integrable real-valued ...
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Is $L^2(\mathbb{R})$ with convolution a Banach Algebra?
Is $L^2(\mathbb{R})$ a Banach algebra, with convolution?
I am pretty sure the answer is no, because I think that
$f,g \in L^2(\mathbb{R})$ does not imply that $f*g \in L^2(\mathbb{R})$. However, I ...
Analyst44
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behaviour of discontinuities after convolution
$f$ is smooth (derivatives of all orders exist) except at $x_1$,$x_2$,$x_3$ where derivatives exist only upto orders of $k_1$,$k_2$,$k_3$ respectively, where $k_i$ is a natural number. Same is the ...
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How this operation is called?
This operation is similar to discrete convolution and cross-correlation, but has binomial coefficients:
$$f(n)\star g(n)=\sum_{k=0}^n \binom{n}{k}f(n-k)g(k) $$
Particularly,
$$a^n\star b^n=(a+b)^n$$...
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Let $f$ be a continuous but nowhere differentiable function. Is $f$ convolved with mollifier, a smooth function?
Let $f$ be a continuous but nowhere differentiable function. Is $f$ convolved with mollifier, a smooth function?
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