This description of the CIC decimator and interpolator is based closely on that provided in An Economical Class of Digital Filters for Decimation and Interpolation, IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. ASSP-29, No. 2, April 1981. The general concept of a CIC filter is the low-pass response that results from filtering an input signal with a cascade of N unit-amplitude, rectangular windows of length R*M. The system response of such filter is:
or
where
- N is the number of CIC stages
- R is the rate change (decimation or interpolation)
- M is the differential delay in the comb section stages of the filter
The implementation of this filter response with a clever combination of comb filter sections, integrator sections, and up-sampling (for interpolation) and down-sampling (for decimation) gives rise to the hardware-efficient implementation of CIC filters.