Any periodic signal decomposes into harmonic sinusoids at integer multiples of a fundamental frequency.

Evidence

Fourier’s Theorem is now usually stated as: … Any periodic function can be represented as an infinite sum of harmonic sinusoids multiplied by appropriate coefficients. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 2732

Categorization

• DEFINE: Precise statement of Fourier’s Theorem as the foundation for all spectral analysis in acoustics.
• XREF: Connects to the practice of frequency-domain analysis familiar from signal processing and audio engineering. — connects to: Any complex tone is decomposable into sine wave components displayed as a spectrum — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 449