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...
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".
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 ...
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 and g?
It might be worthwhile asking the moderators to migrate this question to dsp.SE. With regard to your question about the limits on the integral for calculating convolutions, there is not a single integral that you have to compute, but different integrals depending on your choice for the argument of the function that is the result of the convolution. For a detailed exposition of how to go about ...
