Cascaded integrator–comb filter
In digital signal processing, a cascaded integrator–comb (CIC) is a computationally efficient class of low-pass finite impulse response (FIR) filter that chains N number of integrator and comb filter pairs (where N is the filter's order) to form a decimator or interpolator.
Figure 1) has the reverse order of this architecture, but with the down-sampler replaced with a zero-stuffer (up-sampler).
[1][2] CIC filters were invented by Eugene B. Hogenauer in 1979[3] (published in 1981), and are a class of FIR filters used in multi-rate digital signal processing.
Unlike most FIR filters, it has a down-sampler or up-sampler in the middle of the structure, which converts between the high sampling rate of
used by the integrator stages and the low sampling rate of
[note 1] To see this, consider how a simple moving average filter can be implemented recursively by adding the newest sample
Higher-order CIC structures are obtained by cascading
identical simple moving average filters, then rearranging the sections to place all integrators first (decimator) or combs first (interpolator).
Such rearrangement is possible because both the combs, the integrators, and the entire structure are linear time-invariant (LTI) systems.
In the interpolating CIC, its upsampler (which normally precedes an interpolation filter) is passed through the comb sections using a Noble identity, reducing the number of delay elements needed by a factor of
CIC filters have some appealing features: In the z-domain, each integrator contributes one pole at DC (
Nth-order CIC filters have N times as many poles and zeros in the same locations as the 1st-order.
Thus, the 1st-order CIC's frequency response is a crude low-pass filter.
The main lobes drop off as it reaches the next zero, and is followed by a series of successive lobes that have smaller and smaller peaks, separated by the subsequent zeros.
SincN filters are commonly used with delta-sigma modulation ADCs just prior to downsampling to the desired output data rate (ODR) of
[6] The CIC filter's possible range of responses is limited by this shape.
A short to moderate length FIR or infinite impulse response (IIR) filter can compensate for the falling slope of a CIC filter's shape.
[5] Multiple interpolation and decimation rates can reuse the same set of compensation FIR coefficients, since the shape of the CIC's main lobe changes very little when the decimation ratio is changed.
