The Fourier transform measures how a signal matches each sinusoid pair

Evidence

An interpretation of what the Fourier transform does is that it is a correlation (a kind of similarity comparison, defined by Equation (3.26a)) of the signal x(·) to be transformed with a pair of sinusoids, a sine and a cosine, together expressed as a complex exponential e−jωt or e−jk(2π/N)n. — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 369

Categorization

• DEFINE: Gives an intuitive, non-formulaic gloss of the Fourier transform as correlation with sine/cosine basis functions — useful for explaining spectral analysis.
• CANDY: Clean elevator-summary of what a Fourier transform actually does, good for explaining DSP to non-engineers.
• XREF: connects to: Any waveform can be exactly modeled by combining sine waves — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 443