What is convolution?

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Күн бұрын

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@iabervon Ай бұрын

One day in my ~applied odes class, the TA made the off-hand comment that convolution is like a dot product in an uncountably infinite number of dimensions. Thinking about how that's true and how it's different was really useful to me for developing an intuition for convolutions. (I was also amazed by how much it sounds like technobabble but actually helps to remember the formula.)

@nestorv7627 Ай бұрын

If you take discrete signal processing, the convolution is exactly this, but the dimensions are countable. If you take continuous signal processing, the convolution becomes what dr peyam explained in the video

@elyepes19 Ай бұрын

Many, many deconvoluted thanks for your valuable videos Dr Peyam

@nestorv7627 Ай бұрын

Convolution is an operation that determines how one function influences another function on a point-by-point basis, especially useful when a function is not discrete (i.e. continuous). Like someone else mentioned, it's like an infinite-dimensional dot product. Examples include: impulse response functions in electrical engineering signals. the distribution of the addition of two random variables in probability

@drpeyam Ай бұрын

I really like this explanation, thank you!!

@theproofessayist8441 Ай бұрын

Thank you for the demo. You are going above and beyond. Also love how the point of this video is hmmm we have a theorem or statement that does not work (or is nice) - let's tweak our definition of multiplication so that it is true and indeed convolution is our gal we need! :)

@drpeyam Ай бұрын

Thanks for watching!

@hehehepaitachato9184 Ай бұрын

Thanks for the class, Dr Peyam! I've already seen this before on ODE classes, but never understood so profoundly

@shieldmytears Ай бұрын

Yayyy you actually did it !! Thank you Dr. Peyam💕

@drpeyam Ай бұрын

My pleasure 😊

@YouTube_username_not_found Ай бұрын

What's more interesting is the fact that multiplication of time-functions gets transformed into convolution of frequency-functions. Edit: I omitted a factor of 1/(2i×pi) and other details, they could be found in the Laplace transform article on Wikipedia, in the section "properties and theorems". Also, doesn't the star symbol represent cross-correlation? Isn't convolution denoted by an asterisk? At least that's what I noticed in other sources. Last thing, it would be a good exercise to find all pairs of functions that make the LT of multiplication equal the multiplication of LTs.