CIC Compensation Decimator

Compensate for CIC filter using FIR decimator

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Libraries:
DSP System Toolbox / Filtering / Multirate Filters

Description

The CIC Compensation Decimator block uses an FIR polyphase decimator as the compensation filter. CIC compensation decimators are multirate FIR filters that you cascade with CIC decimators to mitigate the drawbacks of the CIC filters.

CIC decimation filters are used in areas that require high decimation. 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:

  $$abs{\left(\frac{\sin \left(M\frac{\omega }{2}\right)}{\sin \left(\frac{\omega }{2}\right)}\right)}^n$$

  • M — Differential delay

  • n — Number of stages

  • ω — Normalized angular frequency

• CIC filters have a wide transition region.

The compensation decimator filters have an inverse passband response to correct for the CIC droop, and they have a narrow transition width.

This block brings the capabilities of the dsp.CICCompensationDecimator System object™ to the Simulink^® environment.

Ports

Input

Input — Data input

vector | matrix

Specify the data input as a vector or a matrix.

The block treats a P-by-Q input matrix as Q independent channels, decimating each channel over the first dimension.

When you input a variable-size signal (frame length changes during simulation), the frame length of the signal P can be arbitrary, that is, the input frame length does not have to be a multiple of the decimation factor. When you input a fixed-size signal (frame length does not change during simulation), the frame length can be arbitrary only when you select the Allow arbitrary frame length for fixed-size input signals parameter.

Data Types: single | double | int8 | int16 | int32 | int64 | fixed point

Output

Output — Filtered and downsampled signal

vector | matrix

Filtered and downsampled signal, returned as a vector or matrix.

The output signal dimensions depend on the input signal dimensions, the decimation factor of the compensator, and whether you select the Allow arbitrary frame length for fixed-size input signals parameter.

When the output is fixed-point, it is signed only.

This table provides more information on the dimensions of the output signal when you input a fixed-size input signal and a variable-size input signal.

Input Signal Size	Input Signal Dimensions	Output Signal Dimensions
Fixed	P-by-1 column vector, where P is a multiple of the decimation factor M	(P/M)-by-1
Fixed	P-by-1 column vector, where P is not a multiple of the decimation factor M	ceil(P/M)-by-1 when you select Allow arbitrary frame length for fixed-size input signals. If you do not select Allow arbitrary frame length for fixed-size input signals, the block errors.
Fixed	P-by-Q matrix, where P is a multiple of the decimation factor M	(P/M)-by-Q
Fixed	P-by-Q matrix, where P is not a multiple of the decimation factor M	ceil(P/M)-by-Q when you select Allow arbitrary frame length for fixed-size input signals. If you do not select Allow arbitrary frame length for fixed-size input signals, the block errors.
Variable	P-by-Q	ceil(P/M)-by-Q Allow arbitrary frame length for fixed-size input signals parameter appears in the block dialog box but does not have any impact on the input frame length. You can input a variable-size signal of any frame length even if you do not select the Allow arbitrary frame length for fixed-size input signals parameter.

Data Types: single | double | int8 | int16 | int32 | int64 | fixed point

Parameters

Main Tab

Rate change factor — Rate-change factor of the CIC filter

2 (default) | positive integer

Specify the rate-change factor of the CIC filter as a positive integer. The block compensates the CIC filter using an FIR polyphase decimator as the compensation filter.

Number of sections — Number of sections in the CIC filter

2 (default) | positive integer

Specify the number of decimator and comb sections in the CIC filter as a positive integer. The block compensates the CIC filter using an FIR polyphase decimator as the compensation filter.

Differential delay — Differential delay of the CIC filter

1 (default) | positive integer

Specify the delay value used in each comb section of the CIC filter as a positive integer. The block compensates the CIC filter using an FIR polyphase decimator as the compensation filter.

Decimation factor — Decimation factor of compensation filter

2 (default) | positive integer scalar

Specify the decimation factor M of the compensation filter as a positive integer. The number of input rows must be a multiple of the decimation factor.

Minimum order filter design — Design compensation filter of minimum order or of specified order

on (default) | off

When you select this check box, the block designs filter with the minimum order that meets the passband frequency, stopband frequency, passband ripple, and stopband attenuation specifications. When you clear this check box, the block designs filter with the order that you specify in the Filter order parameter.

By default, this check box is selected.

Filter order — Order of compensation filter

12 (default) | positive integer

Specify the order of the compensation filter as a positive integer.

Dependency

To enable this parameter, clear the Minimum order filter design parameter.

Passband edge frequency (Hz) — Passband edge frequency of compensation filter

100000 (default) | positive scalar

Specify the passband edge frequency of the compensation filter as a positive scalar in Hz or in normalized frequency units (since R2024a).

If you set the Sample rate mode parameter to:

• Specify on dialog or Inherit from input port –– The value of the passband edge frequency is in Hz and must be in the range Fpass < Fstop < Fs/2, where Fstop is the stopband edge frequency and Fs is the input sample rate that you specify through the Input sample rate (Hz) parameter.

• Use normalized frequency (0 to 1) –– The value of the passband edge frequency is in normalized frequency units and must be in the range Fpass < Fstop < 1.0.

(since R2024a)

Stopband edge frequency (Hz) — Stopband edge frequency of compensation filter

400000 (default) | positive scalar

Specify the stopband edge frequency of the compensation filter as a positive scalar in Hz or in normalized frequency units (since R2024a).

If you set the Sample rate mode parameter to:

• Specify on dialog or Inherit from input port –– The value of the stopband edge frequency is in Hz and must be in the range Fpass < Fstop < Fs/2, where Fpass is the passband edge frequency and Fs is the input sample rate that you specify through the Input sample rate (Hz) parameter.

• Use normalized frequency (0 to 1) –– The value of the stopband edge frequency is in normalized frequency units and must be in the range Fpass < Fstop < 1.0.

(since R2024a)

Dependency

To enable this parameter, select the Minimum order filter design parameter.

Passband ripple (dB) — Passband ripple of compensation filter

0.1 (default) | positive real scalar

Specify the passband ripple of the compensation filter as a positive real scalar in dB.

Stopband attenuation (dB) — Stopband attenuation of compensation filter

60 (default) | positive real scalar

Specify the stopband attenuation of the compensation filter as a positive real scalar in dB.

Sample rate mode — Mode to specify the input sample rate

Use normalized frequency (0 to 1) (default) | Specify on dialog | Inherit from input port

Since R2024a

Specify the input sample rate using one of these options:

• Use normalized frequency (0 to 1) –– Specify the passband edge and the stopband edge frequencies in normalized frequency units (0 to 1).

• Specify on dialog –– Specify the input sample rate in the block dialog box using the Input sample rate (Hz) parameter.

• Inherit from input port –– The block inherits the sample rate from the input signal.

Input sample rate (Hz) — Sample rate of input signal

1200000 (default) | positive real scalar

Specify the sample rate of the input signal as a positive real scalar in Hz.

Dependencies

To enable this parameter, set the Sample rate mode parameter to Specify on dialog. (since R2024a)

Allow arbitrary frame length for fixed-size input signals — Allow arbitrary frame length for fixed-size input signals

off (default) | on

Since R2023a

Specify whether fixed-size input signals (whose size does not change during simulation) can have an arbitrary frame length, where the frame length does not have to be a multiple of the decimation factor. The block uses this parameter setting only for fixed-size input signals and ignores this parameter if the input has a variable-size.

When the input signal is a variable-size signal, the signal can have arbitrary frame length, that is, the frame length does not have to be a multiple of the decimation factor.

For fixed-size input signals, if you:

• Select the Allow arbitrary frame length for fixed-size input signals parameter, the frame length of the signal does not have to be a multiple of the decimation factor. If the input is not a multiple of the decimation factor, then the output is generally a variable-size signal. Therefore, to support arbitrary input size, the block must also support variable-size operations, which you can enable by selecting the Allow arbitrary frame length for fixed-size input signals parameter.

• Clear the Allow arbitrary frame length for fixed-size input signals parameter, the input frame length must be a multiple of the decimation factor.

View Filter Response — View Filter Response

button (default)

Click this button to open the Filter Visualization Tool FVTool and display the magnitude and phase response of the CIC Compensation Decimator. The response is based on the values you specify in the block parameters dialog box. Changes made to these parameters update FVTool.

To view the magnitude response and phase response simultaneously, click the Magnitude and Phase responses button on the toolbar.

Simulate using — Type of simulation to run

Interpreted execution (default) | Code generation

Specify the type of simulation to run. You can set this parameter to:

• Interpreted execution –– Simulate model using the MATLAB^® interpreter. This option shortens startup time.

• Code generation –– 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 subsequent simulations.

Data Types Tab

Rounding mode — Rounding mode for output fixed-point operations

Floor (default) | Ceiling | Convergent | Nearest | Round | Simplest | Zero

Select the rounding mode for fixed-point operations. The default is Floor.

Coefficients — Word and fraction lengths of coefficients

fixdt(1,16) (default) | fixdt(1,16,0)

Specify the fixed-point data type of the coefficients as one of the following:

• fixdt(1,16) (default) — Signed fixed-point 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 fixed-point data type of word length 16 and fraction length 0. You can change the fraction length to any other integer value.

• <data type expression> — Specify the coefficients data type by using an expression that evaluates to a data type object. For example, numerictype(fixdt([ ],16, 15)). Specify the sign mode of this data type as [ ] or true.

• Refresh Data Type — Refresh to the default data type.

Click the Show data type assistant button to display the data type assistant, which helps you set the coefficients data type.

See Specify Data Types Using Data Type Assistant (Simulink) for more information.

Block Characteristics

Data Types	double | fixed point | integer | single
Direct Feedthrough	no
Multidimensional Signals	no
Variable-Size Signals	yes
Zero-Crossing Detection	no

Algorithms

The response of a CIC filter is given by:

$$H_{cic}\left(\omega \right)={\left[\frac{\sin \left(\frac{RD\omega }{2}\right)}{\sin \left(\frac{\omega }{2}\right)}\right]}^N$$

R, D, and N are the rate change factor, the differential delay, and the number of sections in the CIC filter, respectively.

After decimation, the CIC response has the form:

$$H_{cic}\left(\omega \right)={\left[\frac{\sin \left(\frac{D\omega }{2}\right)}{\sin \left(\frac{\omega }{2R}\right)}\right]}^N$$

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:

$$H_{ciccomp}\left(\omega \right)={\left[RD\frac{\sin \left(\frac{\omega }{2R}\right)}{\sin \left(\frac{D\omega }{2}\right)}\right]}^N\text{for}\omega \le {\omega }_p<\pi$$

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:

$$H_{ciccomp}\left(\omega \right)\approx {\left[\frac{\left(\frac{D\omega }{2}\right)}{\sin \left(\frac{D\omega }{2}\right)}\right]}^N\text{ = }{\left[sinc\left(\frac{D\omega }{2}\right)\right]}^{-N}\text{for}\omega \le {\omega }_p<\pi$$

This previous equation is the inverse sinc approximation to the true inverse passband response of the CIC filter.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2015b

R2024a: Change in the default value of Simulate using parameter

The default value of the Simulate using parameter is now Interpreted execution. With this change, the block uses the MATLAB interpreter for simulation by default.

R2024a: Support for normalized frequencies

When you set the Sample rate mode parameter to Use normalized frequency (0 to 1), you can specify the passband edge and stopband edge frequencies in normalized frequency units (0 to 1).

R2023a: Support for arbitrary input frame length

This block supports input signals with arbitrary frame lengths when the:

• Input signal is a fixed-size signal (frame length does not change during simulation) and you select the Allow arbitrary frame length for fixed-size input signals parameter

• Input signal is a variable-size signal (frame length changes during simulation)

When this block supports an input signal with an arbitrary frame length, the input frame length does not have to be a multiple of the decimation factor.