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The Fourier Transform: A Signal as a Sum of Sinusoids

The pivot of the whole sub-domain: it converts a waveform, where pitch and vowel colour are hopelessly entangled, into a spectrum where they sit in different places. Every pitch and formant measure downstream is either a Fourier view or a deliberate alternative to one.

Questions this Concept answers

Why is a spectrum more useful than a raw waveform when you want to identify a vowel?

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The Fourier Transform in Signal Processing

The Fourier transform is a mathematical operation, rooted in complex numbers and Euler's formula (e^(iθ) = cos θ + i sin θ), that converts a time-domain signal f(t) into a frequency-domain function F…