Gaussian gating minimizes the bandwidth-duration product for tone bursts.

Evidence

This argument can be reversed to show that when the output of an acoustic system, such as a musical instrument, changes slowly, its spectrum occupies a narrow bandwidth, whereas when it changes quickly, it must occupy a larger bandwidth. This can be due to an increase in the number of harmonics present in the spectrum, as would be the case if the waveform becomes sharper or more spiky. … Figure 1.61 shows the effect of an increasing number of harmonics on a square wave. Or, as in the band-pass case described earlier, it would be due to an increase in the bandwidths occupied by the individual partials, or harmonics, of the sound. This would be the case if the envelope of the sound changed more rapidly. Figures 1.62 and 1.63 compare two similar systems—one with a slow and one with a fast rate of amplitude decay, the latter being due to a higher loss of energy from the system. The figures clearly show that in the system that decays more rapidly, there are more harmonics, and there is a higher bandwidth due to the more rapid change in the sound’s envelope. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 489 (#corroborates, via linked claim)

Categorization

• XREF: connects to: Fast-changing acoustic signals necessarily occupy a wider spectral bandwidth. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 489; Rapid changes in a sound’s amplitude envelope force broader spectral bandwidth; The last echo time sets the minimum width of spectral peaks. (+2 more)

Related

• Rapid changes in a sound’s amplitude envelope force broader spectral bandwidth (similarity 0.89)
• Fast-changing acoustic signals necessarily occupy a wider spectral bandwidth. (similarity 0.87)
• Gaussian-shaped tone bursts minimize spectral splatter in gated tones (similarity 0.84)
• A sound’s time-domain rate of change determines its frequency-domain bandwidth (similarity 0.84)
• Faster sound decay broadens spectral peaks in observed spectra (similarity 0.82)
• Random noise and unpredictable spikes carry maximum information due to flat spectra. (similarity 0.81)
• A filter’s inherent time response is determined by its bandwidth (similarity 0.80)
• Short tone bursts widen in spectrum, so experiments use Gaussian-shaped bursts (similarity 0.79)
• Shorter sounds necessarily have broader spectral bandwidths (similarity 0.78)

Broader Connections

• Fast-changing acoustic signals necessarily occupy a wider spectral bandwidth. #corroborates (0.85) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 489
• Rapid changes in a sound’s amplitude envelope force broader spectral bandwidth #corroborates (0.85)