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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. 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 where is the input sample-rate. That makes it possible to design a FIR filter whose every other coefficient is zero, and whose non-zero coefficients are symmetrical about the center of the impulse response. (See Finite impulse response § Window design method) Both of those properties can be used to improve efficiency of the implementation.^{[1]}^{[2]}

**^**Venosa, Elettra; harris, fredric j.; Palmieri, Francesco A. N. (2011-10-17).*Software Radio: Sampling Rate Selection, Design and Synchronization*. New York: Springer. pp. 91-93. ISBN 9781461401124.**^**Meyer-Baese, Uwe (2007-11-14). "5.4.1".*Digital Signal Processing with Field Programmable Gate Arrays*(3 ed.). New York: Springer. p. 274. ISBN 3540726128.

- Lyons, Richard G. (2010-11-11).
*Understanding Digital Signal Processing*(3 ed.). Prentiss-Hall. ISBN 0137027419. - https://www.dsprelated.com/showarticle/1113.php