definition - What is Convolution? - Mathematics Stack Exchange
Sep 6, 2015 · 3 The definition of convolution is known as the integral of the product of two functions $$ (f*g) (t)\int_ {-\infty}^ {\infty} f (t -\tau)g (\tau)\,\mathrm d\tau$$ But what does the …
Meaning of convolution? - Mathematics Stack Exchange
Oct 26, 2010 · I am currently learning about the concept of convolution between two functions in my university course. The course notes are vague about what convolution is, so I was …
What is convolution, how does it relate to inner product?
Oct 25, 2022 · However, in the original convolution formula, the sign of t t is inversed (what does this sign inversing mean?). My final question is: what is the intuition behind convolution? what …
analysis - History of convolution - Mathematics Stack Exchange
Jul 4, 2015 · It the operation convolution (I think) in analysis (perhaps, in other branch of mathematics as well) is like one of the most useful operation (perhaps after the four …
Why are different operations in mathematics referred to as …
Nov 27, 2024 · Convolution appears in many mathematical contexts, such as signal processing, probability, and harmonic analysis. Each context seems to involve slightly different formulas …
What is the convolution of a function $f$ with a delta function …
Sep 12, 2024 · I am merely looking for the result of the convolution of a function and a delta function. I know there is some sort of identity but I can't seem to find it. $\int_ {-\infty}^ {\infty} f …
Definition of Convolution - Mathematics Stack Exchange
Aug 2, 2023 · I am currently studying calculus, but I am stuck with the definition of convolution in terms of constructing the mean of a function. Suppose we have two functions, $f ...
Can someone intuitively explain what the convolution integral is?
Lowercase t-like symbol is a greek letter "tau". Here it represents an integration (dummy) variable, which "runs" from lower integration limit, "0", to upper integration limit, "t". So, the convolution …
real analysis - On the closedness of $L^2$ under convolution ...
Since the Fourier Transform of the product of two functions is the same as the convolution of their Fourier Transforms, and the Fourier Transform is an isometry on $L^2$, all we need find is an …
Proving commutativity of convolution $(f \\ast g)(x) = (g \\ast f)(x)$
Here is something I've sometimes wondered about. If f g f g are both nonnegative proving commutativity of convolution can be done without a tedious change of variable. Indeed, let X X …