Compensate for CIC filter using FIR interpolator
Filtering/Filter Designs
dspfdesign
The CIC Compensation Interpolator block uses an FIR polyphase interpolator as the compensation filter. CIC compensation interpolators are multirate FIR filters that can be cascaded with CIC interpolators to mitigate the drawbacks of the CIC filters.
CIC interpolation filters are used in areas that require high interpolation. These filters are popular in ASICs and FPGAs, since they do not have any multipliers. CIC filters have two drawbacks:
CIC filters have a magnitude response that causes a droop in the passband region. This magnitude response is:
$$abs{\left(\frac{\mathrm{sin}\left(M\frac{\omega}{2}\right)}{\mathrm{sin}\left(\frac{\omega}{2}\right)}\right)}^{n}$$
M — Differential delay
n — Number of stages
ω — Normalized angular frequency
CIC filters have a wide transition region.
The compensation interpolator filters have an inverse sinc passband response to correct for the CIC droop, and they have a narrow transition width.
This block brings the capabilities of the dsp.CICCompensationInterpolator
System object™ to the Simulink^{®} environment.
Rate change factor for the CIC filter to be compensated, specified as
a positive scalar integer. The default is 2
.
Number of integrator and comb sections of the CIC filter to be
compensated, specified as a positive scalar integer. The default is
2
.
Delay value used in each of the comb sections of the CIC filter to be
compensated, specified as a positive scalar integer. The default is
1
.
Interpolation factor of the compensator, specified as a positive
scalar integer. The default value is 2
.
When you select this check box, the block designs filters with the minimum order that meets the specifications for passband frequency, stopband frequency, passband ripple, and stopband attenuation. When you clear this check box, the block designs filters with the order that you specify in Filter order.
By default, this check box is selected.
Order of the compensation filter, specified as a positive scalar
integer. The default is 12
.
Passband edge frequency of the compensation filter, specified as a
real positive scalar in Hz. Passband edge frequency
(Hz) must be less than F_{s}/2, where F_{s} is the output sample rate. The default is
100000
.
Stopband edge frequency of the compensation filter, specified as a
real positive scalar in hertz. Stopband edge frequency
(Hz) must be less than F_{s}/2, where F_{s} is the output sample rate. The default is
400000
.
Passband ripple of compensation filter, specified as a real positive
scalar in dB. The default is 0.1
.
Stopband attenuation of compensation filter, specified as a real
positive scalar in dB. The default is 60
.
When you select this check box, the block inherits its sample rate from the input signal. When you clear this check box, you must specify the sample rate in Input sample rate (Hz).
Input sample rate, specified as a scalar in Hz. The default is
600000
.
Opens the Filter Visualization Tool FVTool and displays the magnitude/phase response of the CIC Compensation Interpolator. The response is based on the block dialog box parameters. Changes made to these parameters update FVTool.
To update the magnitude response while FVTool is running, modify the dialog box parameters and click Apply.
Type of simulation to run. You can set this parameter to:
Code generation
(default)
Simulate model using generated C code. The first time you
run a simulation, Simulink generates C code for the block. The C code is
reused for subsequent simulations, as long as the model does
not change. This option requires additional startup time but
provides faster simulation speed
than Interpreted
execution
.
Interpreted execution
Simulate model using the MATLAB^{®} interpreter. This option shortens
startup time but has slower simulation speed
than Code
generation
.
Rounding method for the output fixedpoint operations. The rounding
methods are Ceiling
,
Convergent
,
Floor
,
Nearest
, Round
,
Simplest
, and
Zero
. The default is
Floor
.
Fixedpoint data type of the coefficients, specified as one of the following:
fixdt(1,16)
(default) —
Signed fixedpoint data type of word length
16
, with binary point scaling. The
block determines the fraction length automatically from the
coefficient values in such a way that the coefficients
occupy maximum representable range without
overflowing.
fixdt(1,16,0)
— Signed
fixedpoint data type of word length 16
,
fraction length 0
. You can change the
fraction length to any other integer value.
<data type expression>
— Specify the coefficients data type by using the
expression that evaluates to a data type object, for
example, numeric type (fixdt
([
]
,16
,
15
), to specify the coefficients data
type. Specify the sign mode of this data type as [
]
or true.
Refresh Data Type
— Refreshes to
the default data type.
Click the Show data type assistant button to display the data type assistant, which helps you set the stage input parameter.
See Specify Data Types Using Data Type Assistant (Simulink) for more information.
Port  Supported Data Types 

Input 

Output 

dsp.CICCompensationInterpolator  DSP System Toolbox 
CIC Compensation Decimator  DSP System Toolbox 
The response of a CIC filter is given by:
$${H}_{cic}\left(\omega \right)={\left[\frac{\mathrm{sin}\left(\frac{RD\omega}{2}\right)}{\mathrm{sin}\left(\frac{\omega}{2}\right)}\right]}^{N}$$
R, D, and N are the rate change factor, the differential delay, and the number of sections of the CIC filter, respectively.
After decimation, the cic response has the form:okay
$${H}_{cic}\left(\omega \right)={\left[\frac{\mathrm{sin}\left(\frac{D\omega}{2}\right)}{\mathrm{sin}\left(\frac{\omega}{2R}\right)}\right]}^{N}$$
The normalized version of this last response is the one that the CIC compensator needs to compensate. Hence, the passband response of the CIC compensator should take the following form:
$${H}_{ciccomp}\left(\omega \right)={\left[RD\frac{\mathrm{sin}\left(\frac{\omega}{2R}\right)}{\mathrm{sin}\left(\frac{D\omega}{2}\right)}\right]}^{N}\text{for}\text{\hspace{0.17em}}\omega \le {\omega}_{p}<\pi $$
where ω_{p} is the passband frequency of the CIC compensation filter.
Notice that when ω/2R ≪ π, the previous equation for Hciccomp(ω) can be simplified using the fact that sin(x) ≅ x:
$${H}_{ciccomp}\left(\omega \right)\approx {\left[\frac{\left(\frac{D\omega}{2}\right)}{\mathrm{sin}\left(\frac{D\omega}{2}\right)}\right]}^{N}\text{=}{\left[sinc\left(\frac{D\omega}{2}\right)\right]}^{N}\text{for}\text{\hspace{0.17em}}\omega \le {\omega}_{p}\pi $$
This previous equation is the inverse sinc approximation to the true inverse passband response of the CIC filter.