Any waveform can be approximated by summing orthogonal sine waves
Evidence
Fourier analysis is a way of building up a waveform from much simpler bits. There are many ways of building up complex waveforms from simple basic shapes, like rectangles, but Fourier analysis was developed (by a French mathematician called Jean Baptiste Joseph Fourier in 1807) to solve the problem of heat diffusion in a metal bar! His idea was very simple. He built up the more complicated shapes of the functions, or waveforms, that he was studying by using the humble sine wave. He found that by adding together sine waves with different frequencies, phases and amplitudes, he could very accurately approximate the functions he was interested in. He found that using sine waves as a basis for approximation was a very useful thing to do. For a start, different sine wave frequencies were independent from or, more strictly, orthogonal to each other and so could be manipulated, or used in equations, independently of each other. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 440
Categorization
- XREF: Fourier’s heat-diffusion origin connects to my standing interest in how abstract math tools (like trust theory, information frameworks) get born in one domain and migrate to another. — connects to: Only a sinusoid has a single frequency; every other shape contains multiple frequencies; A sum of sinusoids is periodic only if their frequencies share a common divisor; A signal’s autocorrelation is a cosine sum over its sinusoidal partials. (+9 more)
- SHARE: Would send to anyone doing audio engineering or signal processing — the orthogonality point is the load-bearing insight.
- corroborated: 2 independent passages support this claim — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 440
Broader Connections
- Accurate square waves require infinitely many harmonics
#exemplifies(0.95) - Complex real-world sounds can be analyzed via Fourier analysis
#corroborates(0.90) — David Howard, Jamie Angus, coustics and Psychoacoustics, 436