Cascaded-Integrator-Comb-Filter
A Cascaded Integrator Comb filter, abbreviated CIC filter (English for cascaded integrator - differentiator filter) is in the digital signal processing a time and discrete-value digital filter which is used for sample rate conversion between different sampling rates. This type of filter was developed in 1981 by Eugene Hogenauer. CIC filters are among the group of multirate filter.
Function
CIC filters are a special type of FIR filters and can be very beneficial in digital hardware such as FPGAs (English: Field Programmable Gate Array) implement since all the coefficients of the filter "1" and thus not computationally intensive multiplications are necessary. There are only simple addition stages and memory, called taps, to the application. CIC filters are used to convert digital signals between areas with different sampling rates, which have a fixed sampling rate relative to each other and to avoid the mirror spectra occurring and to avoid aliasing.
Since all coefficients in the filter "1" are the same, but the adaptation of the filter properties is very limited. The variations of the filter are limited to the number of individual series connected differentiators integration or which describe the slope of the filter and at the differentiators have a different number of delay stages ( taps) that influence the bandwidth in very coarse steps. In practice, therefore, that combinations of the CIC - filters are used with other filters, in order to obtain the desired transmission characteristics as the sum of the individual filters.
Variants
The CIC filter can be divided into the applications in interpolation and decimation.
Interpolation: These are used to convert a discrete signal sequence of a low sampling rate to a higher sampling rate. The signal values that arise due to the higher output rate between the input samples are interpolated. The forced incurred in the upconversion spectra in the mirror range are suppressed by the CIC filter.
Decimation filters: These filters are used to switch from a high to a low sampling rate. In this case, all the signal components of the input signal that exceed the half sampling rate of output can be suppressed by the filter, in order to avoid aliasing.
Filter structure
In the illustration alongside a CIC interpolation filter is shown. Links recognize the individual differentiators, realized as a comb filter, which may vary in number. Each level represents a high-pass, which rises in its frequency response at about 6 dB per octave. Plotted is only a memory register (z -1) per level. An increase of two memory registers (z -2) would result in a halving of the bandwidth. Subsequently, in the center of the actual sample rate converter can be seen in this case that converts to a higher sampling rate. When converting intermediate values are replaced by the value 0. The steps to the right are the levels of integration (low pass filter ) is also different in number depending on the application. These steps assume the signal interpolation before the output sequence with the high sampling rate.
A CIC decimation filter differs only in that the levels of integration are interchanged with the differentiators in the order.
Transfer function
The transfer function H ( z) of the CIC filter with respect to the side with the high sampling rate fs is:
Where the parameters mean: