Narrowing a filter’s bandwidth spreads the signal in time, worst near the cut-off.

Evidence

Any form of filtering which reduces the bandwidth of the signal will also spread it over a longer period of time. In most practical filter circuits these time domain effects are most pronounced near the cut-off frequency and become worse as the cut-off becomes sharper. Again, as in the case of filter shape, these effects can extend well into the pass-band of the filter. Note that even the notch filter has a time response, which gets longer as the notch bandwidth reduces. — David Howard, Jamie Angus, coustics and Psychoacoustics, 2397

Categorization

• DEFINE: Names a fundamental bandwidth-versus-time relationship central to applying psychoacoustics to audio work.
• XREF: Analogous to the time-frequency uncertainty relationship met in earlier psychoacoustics chapters.