In digital signal processing, a cascaded integrator–comb (CIC) is a class of FIR filtering that is combined with a decimator or interpolator. Cascaded integrator–comb filters are extremely useful for filtering in broadcast quality systems. These filters are optimized to filter out noise from the signal. The signal is filtered by a combination of integrators and decimators. For example, if a signal goes through a 3-tap integrator, a 4-tap comb filter, a 3-tap integrator, and a 4-tap comb filter, the result is a 6-tap comb filter. This is a typical CIC architecture and is very common in broadcast quality systems.
CIC filters are used in multi-rate processing. An FIR filter is used in a wide array of applications and can be used in multi-rate processing in conjunction with an interpolator or decimator. CIC filters have low pass frequency characteristics, while FIR filters can have low-pass, high-pass, or band-pass frequency characteristics. CIC filters use only addition and subtraction. FIR filters use addition, subtraction, but most FIR filters also require multiplication. CIC filters have a specific frequency roll-off, while low pass FIR filters can have an arbitrarily sharp frequency roll-off.
CIC filters are in general much more economical than general FIR filters, but tradeoffs are involved. In cases where only a small amount of interpolation or decimation is needed, FIR filters generally have the advantage. However, when rates change by a factor of 10 or more, achieving a useful FIR filter anti-aliasing stop band requires many FIR taps.
For large rate changes, a CIC has a significant advantage over an FIR filter with respect to architectural and computational efficiency. Additionally, CIC filters can typically be reconfigured for different rates by changing nothing more than the decimation/interpolation section assuming the bit width of the integrators and comb sections meets certain mathematical criteria based on the maximum possible rate change.
Whereas an FIR filter can use fixed or floating-point math, a CIC filter uses only fixed-point math. This is necessary because, as a recursively implemented FIR filter, a CIC filter relies on the exact cancellation of poles from the integrator sections by zeros from the comb sections. While the reasons are less than intuitive, an inherent characteristic of the CIC architecture is that if fixed bit length overflows occur in the integrators, they are corrected in the comb sections.
The range of filter shapes and responses available from a CIC filter is somewhat limited. Larger amounts of stopband rejection can be achieved by increasing the number of poles. However, doing so requires an increase in bit width in the integrator and comb sections which increases filter complexity. The shape of the filter response provides even fewer degrees of design freedom. For this reason, many real-world filtering requirements cannot be met by a CIC filter alone. However, a CIC filter followed by a short to moderate length FIR or IIR proves highly applicable. Additionally, the FIR filter shape is normalized relative to the CIC's sampling rate at the FIR/CIC interface so one set of FIR coefficients can be used over a range of CIC interpolation and decimation rates.