Every wave-like quantity has an uncertainty principle tying its Fourier transform pair
Evidence
Time and frequency are the Fourier transform pair that concern us in this book. There are many other examples of Fourier transform pairs: quantities that are related by a Fourier transform. Anything that behaves as a wave has an uncertainty principle connecting Fourier transform pairs. — Eric J. Heller, Why You Hear What You Hear- An…, 433
Categorization
- DEFINE: Generalizes the concept of Fourier transform pairs beyond just time-frequency.
- XREF: Connects to the core thesis of the book (hearing = time-frequency analysis) and to quantum mechanics chapter. — connects to: The uncertainty principle relates resonance width to decay time; Every level of the physical universe is vibrational or wavelike; The time-energy uncertainty principle is really a time-frequency uncertainty principle in disguise — Eric J. Heller, Why You Hear What You Hear- An…, 434 (+4 more)
- corroborated: 2 independent passages support this claim — Eric J. Heller, Why You Hear What You Hear- An…, 433
Broader Connections
- A loudspeaker array’s polar pattern is a Fourier transform of its illumination
#exemplifies(0.85) - Quantum uncertainty drives the early universe’s non-uniformity.
#exemplifies(0.75) — Hawking, Stephen, A Brief History of Time, 247 - The Fourier transform pair converts signals between time and frequency domains
#expands(0.72) — David Howard, Jamie Angus, coustics and Psychoacoustics, 440