Gaussian envelopes minimize the bandwidth-duration product of a signal
Evidence
The Gaussian shape represents an optimum trade between the speed of variation in the temporal envelope and the bandwidth of the associated spectrum, in that the product of the bandwidth and duration is a minimum for the Gaussian shape. — Professor Dr.-Ing. Hugo Fastl, Professor Dr.-Ing. Eberhard, Psychoacoustics- Facts and Models, 89
Categorization
Category: Definitional Content
- XREF: This is the uncertainty principle analog for signals — connects to Fourier/Heisenberg uncertainty in physics; same minimum-product idea.
- DEFINE: Defines the Gaussian window as the optimal tradeoff between temporal and spectral compactness.
Related
- Gaussian shapes minimize the bandwidth-duration product (similarity 0.95)
- Gaussian-shaped tone bursts minimize spectral splatter in gated tones (similarity 0.81)