Cascaded integrator-comb

In digital signal processing, a cascaded integrator–comb (CIC) is an optimized class of finite impulse response (FIR) filter combined with an interpolator or decimator.

A CIC filter consists of one or more integrator and comb filter pairs. In the case of a decimating CIC, the input signal is fed through one or more cascaded integrators, then a down-sampler, followed by one or more comb sections (equal in number to the number of integrators). An interpolating CIC is simply the reverse of this architecture, with the down-sampler replaced with a zero-stuffer (up-sampler).

CIC filters were invented by Eugene B. Hogenauer, and are a class of FIR filters used in multi-rate digital signal processing. The CIC filter finds applications in interpolation and decimation. Unlike most FIR filters, it has a decimator or interpolator built into the architecture. The figure at the right shows the Hogenauer architecture for a CIC interpolator.

The system function for the composite CIC filter referenced to the high sampling rate, f_s is:

Where:

Characteristics of CIC Filters

A CIC filter is an efficient implementation of a moving-average filter. To see this, consider how a moving average filter can be implemented recursively by adding the newest sample ${\displaystyle x[n]}$ to the previous result ${\displaystyle y[n-1]}$ and subtracting the oldest sample. Omitting the division by ${\displaystyle RM}$, we have:

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