Editing Bandwidth (signal processing) (section)

=== Ratio bandwidth ===

Ratio bandwidth is defined as the ratio of the upper and lower limits of the band,
<math display="block">B_\mathrm R= \frac {f_\mathrm H}{f_\mathrm L} \, .</math>

Ratio bandwidth may be notated as <math>B_\mathrm R:1</math>.  The relationship between ratio bandwidth and fractional bandwidth is given by,
<math display="block">B_\mathrm F = 2 \frac {B_\mathrm R - 1}{B_\mathrm R + 1} </math> and
<math display="block">B_\mathrm R = \frac {2 + B_\mathrm F}{2 - B_\mathrm F} \, .</math>

Percent bandwidth is a less meaningful measure in wideband applications.  A percent bandwidth of 100% corresponds to a ratio bandwidth of 3:1.  All higher ratios up to infinity are compressed into the range 100–200%.

Ratio bandwidth is often expressed in [[octave]]s (i.e., as a [[frequency level]]) for wideband applications.  An octave is a frequency ratio of 2:1 leading to this expression for the number of octaves, <math display="block">\log_2 \left(B_\mathrm R\right) .</math>