digital signal processing Digital signal processing (DSP) is the use of digital processing, such as by computers or more specialized digital signal processors, to perform a wide variety of signal processing operations. The digital signals processed in this manner are ...

, half-band filters are widely used for their efficiency in multi-rate applications. A half-band filter is a

low-pass filter A low-pass filter is a filter that passes signals with a frequency lower than a selected cutoff frequency and attenuates signals with frequencies higher than the cutoff frequency. The exact frequency response of the filter depends on the filter des ...

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 In digital signal processing, downsampling, compression, and decimation are terms associated with the process of ''resampling'' in a multi-rate digital signal processing system. Both ''downsampling'' and ''decimation'' can be synonymous with ''comp ...

, 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 a

FIR Firs (''Abies'') are a genus of 48–56 species of evergreen coniferous trees in the family (biology), family Pinaceae. They are found on mountains throughout much of North America, North and Central America, Europe, Asia, and North Africa. The ...

filter whose every other coefficient is zero, and whose non-zero coefficients are symmetrical about the center of the impulse response. (See ) Both of those properties can be used to improve efficiency of the implementation.

References

Further reading