A half-band filter is a finite impulse response (FIR) low-pass filter that reduces the maximum bandwidth of sampled data by a factor of 2. 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. In digital signal processing, half-band filters are widely used for their efficiency in multi-rate applications.