A filter’s bandwidth sets how fast its output can change over time

Evidence

A similar argument can used for band-pass filters. In this case, there is a maximum range of frequencies that can be passed around a given frequency. Although the sine waves corresponding to the band-pass frequencies will be passed, and they may be at quite a high frequency, their amplitude envelope cannot vary quickly, as shown in Figure 1.59. This is because the speed of variation of the envelope depends on the number of and total frequency occupied by the sine wave components in the output of the filter, as shown in Figure 1.60. As it is the amplitude variation of the output of a band-pass filter that carries the information, it too has an inherent time response, which is a function of its bandwidth. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 479

Categorization

Category: Causal Relationships

• XREF: Connects to the uncertainty principle tradeoff between frequency and time resolution, echoing the general filtering/temporal-resolution theme running through the broader acoustics literature.

Related

• A filter’s inherent time response is determined by its bandwidth (similarity 0.92)
• A filter’s output speed of change is limited by its bandwidth (similarity 0.92)
• Filter bandwidth limits how fast a band-pass noise envelope can fluctuate (similarity 0.89)
• Good frequency resolution and good time resolution can never coexist (similarity 0.89)
• Narrower signal bandwidth necessarily spreads signals over longer time spans (similarity 0.86)
• No filter can have both fast time response and narrow bandwidth simultaneously. (similarity 0.86)
• Filters and the signal’s time response are physically coupled tradeoffs (similarity 0.86)
• A filter’s time response is set by its bandwidth, not its center frequency (similarity 0.85)
• Fast-changing acoustic signals necessarily occupy a wider spectral bandwidth. (similarity 0.84)
• Narrowing a filter’s bandwidth inevitably spreads the signal in time, harming timbre (similarity 0.83)
• A sound’s time-domain rate of change determines its frequency-domain bandwidth (similarity 0.82)
• Filtering a signal distorts its time response as well as its spectrum (similarity 0.81)
• Filtering a signal to narrow its bandwidth necessarily spreads it in time. (similarity 0.80)
• Narrow-bandwidth equalization causes filters to ring audibly in time (similarity 0.80)
• Wide bandwidth improves temporal perception while low-pass filtering limits it (similarity 0.80)