Hello World

This post exists to prove one thing: a file in the Obsidian vault becomes a page on the site, with wikilinks and math intact and nothing else in between.

A wikilink

Back to the front page. If that link resolves both in Obsidian’s editor and on the deployed site, the content pipeline is wired correctly.

Some math

Inline first: the DFT of a length-$N$ signal is a change of basis, nothing more.

$$X_k=\sum _{n=0}^{N-1}{x}_n{e}^{-i2\pi kn/N}$$

Written that way it looks like an algorithm. Written as $X=Fx$, with $F$ the matrix whose rows are complex exponentials, it looks like what it is — measuring the same vector against a different set of axes.

That reframing is the whole reason this site exists, and it is also why the interactive figures here need no numerical runtime: a change of basis is a matrix multiply, and a matrix multiply is twenty lines of JavaScript.