The datapath in a CIC interpolator also undergoes internal register growth that is a function of all the design parameters: N, M, and R, in addition to the input sample precision B. As shown in An Economical Class of Digital Filters for Decimation and Interpolation, the registers in the comb and integrator sections grow monotonically, with the maximum register size occurring at the output of the last stage (output of the CIC filter). The maximum register width is given by the following equation:
where
indicates the
ceiling operator. The CIC Compiler always sizes the internal stage registers according
to the register growth as described in An Economical Class of
Digital Filters for Decimation and Interpolation. The output of the filter
can be selected to be full or limited precision (with truncation or rounding) to
accommodate an output width specific to an application. Using limited precision does not
affect the internal register sizes; only the final stage output is scaled, and rounded
if required, to provide the selected output width.