Signal Processing Magic (1) -- CIC Filter

In the world of signal processing, there are many elegant schemes. They are beautiful and pragmatic at the same time. Sometime you are wondering how the inventors create them. I feel obliged to introduce them to my audience. Today, let me start from a filter named CIC (Cascaded Integrator–Comb). CIC filter is mainly used for integer up-sampling and down-sampling. The main benefit of this scheme is that no multiplication is needed, which is welcomed in term of hardware complexity.

Figure below shows CIC filter architecture with N stages and decimation rate of R. M is an extra parameter and it can be 1 or 2. Normally M is set as 1. CIC filter can also be used as interpolation and the flow is opposite when used as decimation.

Accordingly, we can write the transfer function of decimation CIC filter as:

\[(\frac{1-z^{-RM}}{1-z^{-1}})^{N}\]


By increasing N with fixed R, the filter can have more rejection.

By increasing R with fixed N, the filter's cutoff frequency decreases proportionally.