Like digital signal processing, such as cell phones, digital receivers, television, CD & DVD players, **half-band filters** are widely used for their efficiency in multi-rate applications. A half-band filter is a lowpass filter that reduces the maximum bandwidth of sampled data by an approximate factor of 2 (one octave). When multiple octaves of reduction are needed, a cascade of half-band filters is common. And when the goal is downsampling, each half-band filter needs to compute only half as many output samples as input samples.

It follows from the filter's definition that its transition region, or *skirt*, can be centered at frequency
f
s
/
4
,
where
f
s
is the input sample-rate. That makes it possible to design an FIR filter whose every other coefficient is zero, and whose non-zero coefficients are symmetrical about the center of the impulse response. (See Window design method) Both of those properties can be used to improve efficiency of the implementation.