Bandwidth

The bandwidth of a filter denotes the range of frequencies the filter allows to pass through. Calculating the bandedge frequencies informs you of the bandwidth's characteristics.

The quality constant Q is defined as the ratio of the bandwidth over the center frequency of the filter. Q remains constant across all octave bands for octave filters. For example, an octave filter with a center frequency of 1,000 Hz leads to the following bandedge frequencies:

f 1 = 1 , 000 2 = 707 ⁢   H z
f 2 = ( 1 , 000 ) ( 2 ) = 1 , 414 ⁢     H z
B W = f 2 − f 1 = 707 ⁢   H z
Q = 707 1 , 000 = 0.707

where

f 1 and f2 are bandedge frequencies

Q is the quality constant

BW is the bandwidth

An octave filter with a center frequency of 8,000 Hz leads to the following bandedge frequencies:

f 1 = 8 , 000 2 = 5 , 657 ⁢   H z
f 2 = ( 8 , 000 ) ( 2 ) = 11 , 314 ⁢     H z
B W = f 2 − f 1 = 5 , 657 ⁢   H z
Q = 5 , 657 8 , 000 = 0.707

where

f 1 and f2 are bandedge frequencies

BW is the bandwidth

Q is the quality constant

The results obtained from calculating the bandedge frequencies indicate the following bandwidth characteristics:

  • The bandwidth of the octave filters is narrow when the center frequency is low.
  • The bandwidth of the octave filters is wider when the center frequency is higher.

Because of the bandwidth characteristics, fractional-octave analysis uses a logarithmic frequency scale to compute and display octave spectra.