An excellent reference to understanding these units is the web article: “The concept of digital frequency,” by Professor Fowler, Department of Electrical Engineering, State University of New York at Binghamton. Note that the frequency axis can be specified in radians/sample, normalized frequency normalized to the sampling rate or half sampling rate (preferred by MATLAB) etc. In addition it has some other interesting properties.
The fewer the multiplications, the lower the cost. This implies that we do not need to do a multiplication for that tap reducing the need for multiplications! A very cost effective and useful property indeed, since multiplication takes time and silicon area. Because of this characteristic every other tap value of this filter is equal to zero. The frequency response of this type of filter is symmetrical about the (1/4)fs point on the frequency axis. And when the goal is downsampling, each half-band filter needs to compute only half as many output samples as input samples.” Wikipedia. When multiple octaves of reduction are needed, a cascade of half-band filters is common. A half-band filter is a low-pass filter that reduces the maximum bandwidth of sampled data by a factor of 2 (one octave). “In digital signal processing, half-band filters are widely used for their efficiency in multi-rate applications. The following discussion presents more details on the half band filter as well as its usage in the decimation filter.
The link is: &i=stripbooks&ref=nb_sb_noss. One of their prime uses is in decimation of multirate digital signals.įor a good basic introduction to FIR filters please read the FIR filter book. Half band filters are useful digital filters that have symmetric impulse responses and generally about half their impulse response consists of 0 (zero) thus allowing for fewer multiplications.
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