CIC filters do not have multipliers and consist of only adders, subtracters, and registers. Therefore, you can implement multirate filters efficiently using the CIC filter structure. CIC filters are defined by the following transfer function:

H ⁢   ( z )     = H I N ⁢ ( z )   H C N ⁢ ( z ) = ( 1 − z − R M )   N ⁢ ( 1 − z − 1 )   N     =   ( ∑ k = 0 R M − 1 z − k ) N  

where

  • z is a complex variable
  • I is a basic integrator section
  • C is a basic comb section
  • M is the sampling frequency conversion factor
  • R is the differential delay
  • N is the number of stages

Theoretically, R and N can be any positive integer value, but the LabVIEW Digital Filter Design Toolkit constrains R to be either 1 or 2 because you do not need to use other values in most cases. N is in the range [1, 8]. The equation above shows that a CIC filter is equivalent to N stages of cascaded FIR filters with unit coefficients. Each FIR filter has a rectangular impulse response. All coefficients of the FIR filters are 1 and therefore symmetric, so the CIC filter has a linear phase response and constant group delay.

Use the Multirate CIC Design Express VI to design a CIC filter.