How Did the Fourier Transform Translate Eridian? A Deeper Insight

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I recently saw Project Hail Mary, and it was amaze amaze amaze! So now, I'm reading the book. In the movie, Grace translates Rocky's language in an unexplained way. We are left to assume some type of ML-based pattern matching. In the book, it is very well explained that Grace uses the Fourier transform to determine which notes/chords are being "spoken" and catalogues them. I'm so happy Andy Weir didn't do any hand-wavy magic. ML solves this nonsense. So, how the heck does this work?

Well, before we answer that lets think of more practical uses. Ever wondered how your phone knows exactly which note you’re singing, or how your Wi-Fi squeezes a Netflix show through the air? It all starts with a mathematical "cheat code" involving circles and matrices.

Meet the "Circulant Matrix" (The Infinite Loop)

Imagine a line of 8 people standing in a circle. You give a...

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