In digital signal processing, half-band filters are widely used for their efficiency in multi-rate applications.
A half-band filter is a low-pass filter that reduces the maximum bandwidth of sampled data by a factor of 2 (one octave).
When multiple octaves of reduction are needed, a cascade of half-band filters is common.
It follows from the filter's definition that its transition region, or skirt, can be centered at frequency
(See Finite impulse response § Window design method) Both of those properties can be used to improve efficiency of the implementation.