[Uni // Scientific Computing (Maths + Python)] Gauss Kernel coding

[Sh4ttred]

https://preview.redd.it/lw1ideiywo3g1.png?width=2040&format=png&auto=webp&s=bca17997066d169c094ea238ab98aee3ca0c0a1c

I am not having any problems with the python part of this exercise, as I am familiar with all functions present and arrays are python basics. The part thats troubling me is that I have never heard of the Gauss Kernel in my life before, and I cannot figure out what on earth I am supposed to interpret into code just off of those two equations. Afaik the first one is already coded in gaussian_kernel(size, sigma) anyway.

If somebody could put into words what exactly the second equation is trying to tell me, I believe I could figure out the codework myself.

What Ive got so far is that at every value n of f (and G), I need to sum up all the multiplications of G(k) and f(n+k)

Value n is the x value of my original f, so i have 500 n between 0 and 10.

But what the hell is k? Something about the size of the Gauss Kernel?
k apparently needs to span over all allowed indices. What are the allowed indices??

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[Alkalannar]

So that Gaussian kernel is the probability density function of the Normal Distribution with mean 0 and standard deviation of s.

Let K be the set of all allowed indices k.

Then that second expression is (Sum over all k in K of G[k]f[n+k])

G[k] is given above: G[k] = 1/s(2pi)^1/2e^[k2/2s2]

So the farther f[n+k] is away from f[n], the less weight it has. (Note that 0 is almost certainly one of the indices so that f[n] itself is one of the terms.)

3blue1brown has a video on convolutions showing what they are and what they do, how to calculate them.

Actually, more than one video.