CIC Interpolation

CIC-filter is an optimized class of linear-phase FIR filters consisting of cascaded comb filters and integrators.

Conceptually, the interpolation CIC filter is an element of increasing the sampling rate, followed by a CIC filter , which is a reconstruction low-pass filter and performs filtering without changing the sampling rate. The interpolation CIC filter increases the sampling rate of the input signal by an integer factor using a cascaded Integrator comb filter (Cascaded Integrator-Comb, CIC).

In a more efficient implementation, a CIC filter that works without changing the sampling rate , is factorized in this way:

Where

In an algorithm that provides full multi-rate filtering, two remarkable identities for interpolation are taken into account, which allow you to move the operation of changing the sampling rate for the cascade of comb filters without distorting the result of the operation.

The transfer function of the resulting filter is given by the following equation:

For a flowchart showing multi-speed implementation, see [algorithms].

The interpolation CIC filter is implemented as a cascade of comb filters, followed by an element of increasing the sampling rate of the signal in once, and then a cascade of integrators.

This diagram shows a cascade of comb filters with two sections and a cascade of integrators with two sections. A single delay in the integrators of the CIC filter can be located both in the direct and feedback circuits. These two configurations provide identical frequency characteristics of the filter. However, the actual numerical sequences in the output for these two configuration options will be different due to the effect of the delay. In this algorithm, a single delay is placed in the path of the direct line of the integrator, since such a configuration is preferable for HDL implementation.