A filter’s transition region can audibly affect frequencies up to an octave away

Evidence

The cutoff frequency of a filter is usually expressed as the point at which it is attenuating the signal by 3 dB relative to the pass-band; see Figure 7.38. Thus if a filter’s cutoff is set to a given frequency, there will be a region within the pass-band that affects the amplitude of the frequency components of the signal. This region can extend as far as an octave away from the cutoff point. Therefore, in practice, the filter’s cutoff frequency must be set beyond the pass-band that one would expect from a simple consideration of the frequency range of the instruments in order to avoid any tonal change due to change in frequency content caused by the filter’s transition region. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 2410

Categorization

• DEFINE: Explains the 3 dB convention for expressing cutoff frequency and why filter roll-off regions matter perceptually.
• XREF: connects to: Filters attenuate gradually over a frequency range rather than cutting sharply — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 471