The Cascade Integrator Comb (CIC) filter is an efficient digital filter used in multi-rate signal processing, characterized by its low-pass filtering properties and several advantages, including the use of coefficients that are all equal to one, which eliminates the need for storage and multiplication during filtering. The structure allows for flexible interpolation settings without affecting the overall design.
The integrator's behavior is described in both time and frequency domains, showing that it has poles at integer multiples of \(2\pi\) and infinite gain for DC signals. The comb filter operates by delaying the input signal, resulting in a frequency response that only has zeros.
For a single-stage CIC filter, the amplitude spectrum is derived from the integrator and comb filter responses, revealing that it achieves zero-pole cancellation. The main lobe width and side lobe levels are also discussed, with side lobe suppression increasing with the number of stages, although this may lead to increased passband ripple.
The maximum gain of a multi-stage CIC filter is expressed as \(G_{max} = (RM)^N\), where \(R\) and \(M\) are parameters defining the filter's structure and \(N\) is the number of stages. The output bit width is calculated to prevent overflow during FPGA design, ensuring efficient resource usage.
