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 functions give? Why are is it being integrated on negative infinity to infinity? What is the physical significance of the convolution?
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 anyone could giv...
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 wrong.
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, subtraction, multiplication, division) MY Question: How old the operation convolution is? In other words, the idea of convolution goes back to whom?
Convolution appears in many mathematical contexts, such as signal processing, probability, and harmonic analysis. Each context seems to involve slightly different formulas and operations: In stand...
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...
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 ...
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, which value for any value of argument (independent variable) "t" is expressed as an integral over dummy variable "tau".
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 $L^2$ function that when squared is no longer an $L^2$ function.
0 We started recently talking in my signal processing class about the convolution integral, and in theory, it sounds easy enough but now after a few exercises I realize I either don't know the technique needed to find the limits of the integral (since you usually need to consider different cases for your integral limits)
