/sci/ - Science & Math

>>9758257
maybe this will help
https://www.youtube.com/watch?v=spUNpyF58BY

and if you know a bit more about math, you could think of it as an inner product of functions
from a linear algebraic point of view, the inner product measures "how close" two vectors are, usually interpreted as an angle
this means that if you take the inner product of a vector and a basis vector, you can see "how much" the basis vector is in the other vector
and remember that you can decompose a vector into a linear combination of basis vectors
in your function space, the basis functions are trigonometric functions, but there are uncountably many of such functions, so that's a hint that you should integrate rather than sum
and that's what the fourier transform does
it takes the inner product of functions, decomposing the input function into its component parts (which are the trigonometric sin/cos functions), and measures how much of each basis function is present in the function

at least i think so?
got me through a complex analysis course so ive been sticking to it