Theory of Communication. Part 1¶
Gabor, D. (1946). Theory of Communication. Part 1: The Analysis of Information. Journal of the Institution of Electrical Engineers - Part III: Radio and Communication Engineering, 93(26), 429-441.
Cited by¶
5 citations across 4 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Conjugate-Observable Complementarity
- In signal processing and time–frequency analysis, a signal cannot be arbitrarily localized in both time and frequency: a pure tone has exact frequency but infinite duration, a brief click has exact timing but smeared spectrum, and the time–bandwidth product is bounded below — the Gabor limit, mathematically isomorphic to the Heisenberg relation.
This sourceDerives the time–frequency (Gabor) limit on simultaneous time and bandwidth localization, mathematically isomorphic to the Heisenberg relation.
- In signal processing and time–frequency analysis, a signal cannot be arbitrarily localized in both time and frequency: a pure tone has exact frequency but infinite duration, a brief click has exact timing but smeared spectrum, and the time–bandwidth product is bounded below — the Gabor limit, mathematically isomorphic to the Heisenberg relation.
Domain-specific¶
Mechanisms¶
- Short-Time Fourier Transform Window Selection
- The trade is fundamental, not a bug to engineer away: the Heisenberg–Gabor limit means no single window resolves arbitrarily fine in both time and frequency at once
This sourceDerives a joint time-frequency uncertainty that prevents arbitrary simultaneous localization and makes resolution in one domain trade against the other.
- The trade is fundamental, not a bug to engineer away: the Heisenberg–Gabor limit means no single window resolves arbitrarily fine in both time and frequency at once
- Wave-Packet Width Shaping
- The analyst shapes the window width to the question: a narrow window to time the rapid terminal-buzz pulses, a wider one to read the frequency sweep of a single cry — honoring the Gabor limit, the time–frequency version of the uncertainty bound, which forbids sharpness in both at once.
This sourceDerives a time–frequency uncertainty relation: improving temporal localization necessarily reduces frequency precision, and vice versa.
- The analyst shapes the window width to the question: a narrow window to time the rapid terminal-buzz pulses, a wider one to read the frequency sweep of a single cry — honoring the Gabor limit, the time–frequency version of the uncertainty bound, which forbids sharpness in both at once.
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