The Fourier transform pair converts signals between time and frequency domains

Evidence

Fourier further theorized that if he combined enough sine waves together he could exactly model any waveform in existence. This allowed him to develop the Fourier transform pair—two equations that provide a means of transforming the time domain into the frequency domain and back. — David Howard, Jamie Angus, coustics and Psychoacoustics, 440

Categorization

• DEFINE: Introduces the Fourier transform pair and the time/frequency domain duality.
• corroborated: 2 independent passages support this claim — David Howard, Jamie Angus, coustics and Psychoacoustics, 440
• XREF: connects to: Whether echoes constructively add in Fourier analysis depends on wavelength relative to echo timing.; Frequency measured in Hertz is dimensionally inverse seconds; Real signals contain smooth distributions of infinite frequencies (+8 more)

Broader Connections

• A loudspeaker array’s polar pattern is a Fourier transform of its illumination #expands (0.82)
• The Fourier transform unwinds periodic signals into flat DC #expands (0.78)