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 product of 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 wondering if …
What is convolution, how does it relate to inner product?
Oct 25, 2022 · My final question is: what is the intuition behind convolution? what is its relation with the inner product? I would appreciate it if you include the examples I gave above and correct me if I am …
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 fundamental operations addition, …
What is the convolution of a function $f$ with a delta function $\delta$?
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 (u-x)\delta...
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 is a function, …
Proving commutativity of convolution $ (f \ast g) (x) = (g \ast f) (x)$
But we can still find valid Laplace transforms of f (t) = t and g (t) = (t^2). If we multiply their Laplace transforms, and then inverse Laplace transform the result, shouldn't the result be a convolution of f …
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 $L^2$ …
Calculate convolution y[n] = (x ∗ h)[n] of signals h[n] and x[n]
Jan 20, 2017 · 0 As a response to your question, let me explain the equation, which is discrete convolution: \begin {equation} y [n]=x [n]\ast h [n] \quad = \sum_ {k=-\infty}^ {\infty}x [k]h [n-k] \end …