What frequencies are inside a sound? Fourier Transform | Curious Engineering #01

Instructor: Dr. Süleyman Burak ÇELİK

The single curve that reaches a microphone is really a weighted sum of pure sine waves. In this episode we take that sum apart step by step: we split the wave into its components, watch the "multiply and average" mechanism of the Fourier transform run live, see how harmonics set pitch and timbre, and then rebuild the wave from nothing but a list of amplitudes. Covered in this episode • Period and fundamental frequency (two hundred twenty hertz, the note A) • Why the amplitudes fall off roughly as one over n • Orthogonality: why the average product of two different sines is zero • The amplitude spectrum of the discrete Fourier transform (DFT) • Same pitch, different timbre: sawtooth, clarinet, flute • Why a clarinet’s even harmonics are so weak • The Gibbs phenomenon: why a sharp jump never resolves with finitely many components • What amplitude and phase say together