I have been watching videos from 3Blue1brown guy on youtube. He explains that the fourier transform is an unscaled version of calculating the centre of mass of a graph.
ref: https://www.youtube.com/watch?v=spUNpyF58BY
But I don't think the intuition is correct because $g(t)e^{-iwt}$ refers to the original graph Whereas $g(t)$ should be the winded or augmented graph if you want to calculate the centre of mass.
g(t) is the unknown graph
w = 2pif
In his video he explaains that given an unknown graph, you winded it around a circle and then calculate the frequency of the winded graph. When the frequency fo that graph matches the frequency of the unknown graph the centre of mass deviates from the origin.
Has anyone heard this intuition before?
