CIC Frequency Response

The frequency response (in dB) of the CIC follows the following formula:

where

R = CIC Interpolation Rate

f = Frequency (fraction of CIC input sample rate)

The following diagram shows the response of a six stage CIC filter with 8x interpolation.

Notice that the frequency response has a significant amount of roll-off in the passband. You must compensate for CIC roll-off in custom FIR filters in order to obtain an overall flat response.