dsphdl.CICDecimator

Decimate signal using CIC filter

Description

The dsphdl.CICDecimator System object™ decimates an input signal by using a cascaded integrator-comb (CIC) decimation filter. CIC filters are a class of linear phase finite impulse response (FIR) filters consisting of a comb part and an integrator part. The CIC decimation filter structure consists of N sections of cascaded integrators, a rate change factor of R, and N sections of cascaded comb filters. For more information about CIC decimation filters, see Algorithms.

The System object supports these combinations of input and output data.

• Scalar input and scalar output — Support for fixed and variable decimation rates

• Vector input and scalar output — Support for fixed decimation rates only

• Vector input and vector output — Support for fixed decimation rates only

The System object provides an architecture suitable for HDL code generation and hardware deployment.

The System object supports real and complex fixed-point inputs.

To filter input data with an HDL-optimized CIC decimation filter, follow these steps:

1. Create the dsphdl.CICDecimator object and set its properties.

2. Call the object with arguments, as if it were a function.

To learn more about how System objects work, see What Are System Objects?

Note

You can also generate HDL code for this hardware-optimized algorithm, without creating a MATLAB^® script, by using the DSP HDL IP Designer app. The app provides the same interface and configuration options as the System object.

Creation

Syntax

cicDecFilt = dsphdl.CICDecimator

cicDecFilt = dsphdl.CICDecimator(Name=Value)

Description

cicDecFilt = dsphdl.CICDecimator creates an HDL-optimized CIC decimation filter System object, cicDecFilt, with default properties.

cicDecFilt = dsphdl.CICDecimator(Name=Value) creates the filter with properties set using one or more name-value arguments.

Properties

Unless otherwise indicated, properties are nontunable, which means you cannot change their values after calling the object. Objects lock when you call them, and the release function unlocks them.

If a property is tunable, you can change its value at any time.

For more information on changing property values, see System Design in MATLAB Using System Objects.

DecimationSource — Source of decimation factor

'Property' (default) | 'Input port'

Specify whether the System object operates with a fixed or variable decimation rate.

• 'Property' — Use a fixed decimation rate specified by the DecimationFactor property.

• 'Input port' — Use a variable decimation rate specified by the R input argument.

For vector inputs, the System object does not support a variable decimation rate.

DecimationFactor — Decimation factor

2 (default) | integer from 1 to 2048

Specify the decimation factor as an integer from 1 to 2048. This value gives the rate at which the System object decimates the input.

Dependencies

To enable this property, set the DecimationSource property to 'Property'.

MaxDecimationFactor — Upper bound of variable decimation factor

2 (default) | integer from 1 to 2048

Specify the upper bound of the range of valid values for the R input argument as an integer from 1 to 2048.

Note

For vector inputs, the System object does not support variable decimation.

Dependencies

To enable this property, set the DecimationSource property to 'Input port'.

DifferentialDelay — Differential delay

1 (default) | 2

Specify the differential delay of the comb part of the filter as either 1 or 2 cycles.

NumSections — Number of integrator or comb sections

2 (default) | 1 | 3 | 4 | 5 | 6

Specify the number of sections in either the integrator or the comb part of the System object.

GainCorrection — Output gain compensation

false (default) | true

Set this property to true to compensate for the output gain of the filter.

The latency of the System object varies depending on the type of input, the decimation you specify, the number of sections, and the value of this property. For more information on the latency of the System object, see Latency.

OutputDataType — Data type of output

'Full precision' (default) | 'Same word length as input' | 'Minimum section word lengths'

Choose the data type of the filtered output data.

• 'Full precision' — The output data type has a word length equal to the input word length plus gain bits.

• 'Same word length as input' — The output data type has a word length equal to the input word length.

• 'Minimum section word lengths' — The output data type uses the word length you specify in the OutputWordLength property. When you choose this option, the System object applies a pruning algorithm internally. For more information about pruning, see Output Data Type.

OutputWordLength — Word length of output

16 (default) | integer from 2 to 104

Word length of the output, specified as an integer from 2 to 104.

Note

When this value is 2, 3, 4, 5, or 6, the System object can overflow the output data.

Dependencies

To enable this property, set the OutputDataType property to 'Minimum section word lengths'.

ResetInputPort — Reset argument

false (default) | true

When you set this property to true, the System object expects a reset input argument.

Usage

Syntax

[dataOut,validOut] = cicDecFilt(dataIn,validIn)

[dataOut,validOut] = cicDecFilt(dataIn,validIn,R)

[dataOut,validOut] = cicDecFilt(dataIn,validIn,reset)

[dataOut,validOut] = cicDecFilt(dataIn,validIn,R,reset)

Description

[dataOut,validOut] = cicDecFilt(dataIn,validIn) filters and decimates the input data using a fixed decimation factor only when validIn is true.

[dataOut,validOut] = cicDecFilt(dataIn,validIn,R) filters the input data using the specified variable decimation factor R. The DecimationSource property must be set to 'Input port'.

[dataOut,validOut] = cicDecFilt(dataIn,validIn,reset) filters the input data when reset is false and clears filter internal states when reset is true. The System object expects the reset argument only when you set the ResetInputPort property to true.

[dataOut,validOut] = cicDecFilt(dataIn,validIn,R,reset) filters the input data when reset is false and clears filter internal states when reset is true. The System object expects the reset argument only when you set the ResetInputPort property to true. The DecimationSource property must be set to 'Input port'.

Input Arguments

dataIn — Input data

scalar | column vector

Specify input data as a scalar or a column vector with a length from 1 to 64. The input data must be a signed integer or signed fixed point with a word length less than or equal to 32. The DecimationFactor property must be an integer multiple of the input frame size.

While processing the input data, the System object implements the rounding method Floor and the overflow action Wrap. For more details, see Rounding Modes and Overflow Handling.

Data Types: int8 | int16 | int32 | fi
Complex Number Support: Yes

validIn — Indicates valid input data

scalar

Control signal that indicates if the input data is valid. When validIn is 1 (true), the object captures the values from the dataIn argument. When validIn is 0 (false), the object ignores the values from the dataIn argument.

Data Types: logical

R — Variable decimation rate

scalar

Specify the decimation rate.

The R value must have the data type fi(0,12,0) and it must be an integer in the range from 1 to the MaxDecimationFactor property value.

Dependencies

To enable this argument, set the DecimationSource property to 'Input port'.

Data Types: fi(0,12,0)

reset — Clears internal states

logical scalar

Control signal that clears internal states. When reset is 1 (true), the object stops the current calculation and clears internal states. When the reset is 0 (false) and the input valid is 1 (true), the object captures data for processing.

For more reset considerations, see the Reset Signal section on the Hardware Control Signals page.

Dependencies

To enable this argument, set the ResetInputPort property to true.

Data Types: logical

Output Arguments

dataOut — CIC-decimated output data

scalar | column vector

CIC-decimated output data, returned as a scalar or a column vector with a length from 1 to 64.

The OutputDataType property sets the data type of this argument. See Output Data Type.

Data Types: int8 | int16 | int32 | fi
Complex Number Support: Yes

validOut — Indicates valid output data

scalar

Control signal that indicates if the output data is valid. When validOut is 1 (true), the object returns valid data from the dataOut argument. When validOut is 0 (false), values from the dataOut argument are not valid.

Data Types: logical

Object Functions

To use an object function, specify the System object as the first input argument. For example, to release system resources of a System object named obj, use this syntax:

release(obj)

Specific to dsphdl.CICDecimator

getLatency

Latency of CIC decimation filter

Common to All System Objects

step	Run System object algorithm
release	Release resources and allow changes to System object property values and input characteristics
reset	Reset internal states of System object

Examples

Create CIC Decimation Filter for HDL Code Generation

This example shows how to use a dsphdl.CICDecimator System object™ to filter and downsample data. This object supports scalar and vector inputs. In this example, two functions are provided to work with scalar and vector inputs separately. You can generate HDL code from these functions.

Generate Frames of Random Input Samples

Set up workspace variables for the object to use. The object supports fixed and variable decimation rates for scalar inputs and only a fixed decimation rate for vector inputs. The example runs the HDLCIC_maxR8 function when you set the scalar variable to true and runs the HDLCIC_vec function when you set the scalar variable to false. For scalar inputs, choose a range of the input varRValue values and set the decimation factor value R to the maximum expected decimation factor. For vector inputs, the input data must be a column vector of size 1 to 64 and R must be an integer multiple of the input frame size.

R = 8;             % decimation factor
M = 1;             % differential delay
N = 3;             % number of sections
scalar = true;     % true for scalar; false for vector
if scalar
    varRValue = [2, 4, 5, 6, 7, 8];
    vecSize = 1;
else
    varRValue = R; %#ok
    fac = (factor(R));
    vecSize = fac(randi(length(fac),1,1));
end

numFrames = length(varRValue);
dataSamples = cell(1,numFrames);
varRtemp = cell(1,numFrames);
framesize = zeros(1,numFrames);
refOutput = [];
WL = 0;            % Word length
FL = 0;            % Fraction length

Generate Reference Output from dsp.CICDecimator System Object

Generate frames of random input samples and apply the samples to the dsp.CICDecimator System object. Later in this example, you use the output generated by the System object as reference data for comparison. The System object does not support a variable decimation rate, so you must create and release the object for each change in decimation factor value.

totalsamples = 0;
for i = 1:numFrames
    framesize(i) = varRValue(i)*randi([5 20],1,1);
    dataSamples{i} = fi(randn(vecSize,framesize(i)),1,16,8);
    ref_cic = dsp.CICDecimator(DifferentialDelay=M, ...
                               NumSections=N, ...
                               DecimationFactor=varRValue(i));
    refOutput = [refOutput,ref_cic(dataSamples{i}(:)).']; %#ok
    release(ref_cic);
end

Run Function Containing dsphdl.CICDecimator System Object

Set the properties of the System object to match the input data parameters and run the function for your input type. These functions operate on a stream of data samples rather than a frame. You can generate HDL code from these functions.

The example uses the HDLCIC_maxR8 function for a scalar input.

function [dataOut,validOut] = HDLCIC_maxR8(dataIn,validIn,R)
%HDLCIC_maxR8
% Performs CIC decimation with an input decimation factor up to 8. 
% dataIn is a scalar fixed-point value.
% validIn is a logical scalar value.

  persistent cic8;
  if isempty(cic8)
    cic8 = dsphdl.CICDecimator(DecimationSource='Input port', ...
                               MaxDecimationFactor=8, ...
                               DifferentialDelay=1, ...
                               NumSections=3);
  end    
  [dataOut,validOut] = cic8(dataIn,validIn,R);
end
% Copyright 2021-2023 The MathWorks, Inc.

The example uses the HDLCIC_vec function for a vector input.

function [dataOut,validOut] = HDLCIC_vec(dataIn,validIn)
%HDLCIC_vec
% Performs CIC decimation with an input vector. 
% dataIn is a fixed-point vector.
% validIn is a logical scalar value.

  persistent cicVec;
  if isempty(cicVec)
    cicVec = dsphdl.CICDecimator(DecimationSource='Property', ...
                                 DecimationFactor=8, ...
                                 DifferentialDelay=1, ...
                                 NumSections=3);
  end    
  [dataOut,validOut] = cicVec(dataIn,validIn);
end
% Copyright 2021-2023 The MathWorks, Inc.

To flush the remaining data, run the object by inserting the required number of idle cycles after each frame using the latency variable. For more information, see Latency.

Initialize the output to a size large enough to accommodate the output data. The final size is smaller than totalsamples due to decimation.

latency = floor((vecSize - 1)*(N/vecSize)) + 1 + N + (2+(vecSize+1)*N) + 9;
dataOut = zeros(1,totalsamples+numFrames*latency);
validOut = zeros(1,totalsamples+numFrames*latency);
idx=0;
for ij = 1:numFrames
    if scalar
        % scalar input with variable decimation
        for ii = 1:length(dataSamples{ij})
            idx = idx+1;
            [dataOut(idx),validOut(idx)] = HDLCIC_maxR8( ...
                dataSamples{ij}(ii), ...
                true, ...
                fi(varRValue(ij),0,12,0));
        end
        for ii = 1:latency
            idx = idx+1;
            [dataOut(idx),validOut(idx)] = HDLCIC_maxR8( ...
                fi(0,1,16,8), ...
                false, ...
                fi(varRValue(ij),0,12,0));
        end

    else
        % vector input with fixed decimation
        for ii = 1:size(dataSamples{ij},2) %#ok
            idx = idx+1;
            [dataOut(idx),validOut(idx)] = HDLCIC_vec( ...
                dataSamples{ij}(:,ii), ...
                true);
        end
        for ii = 1:latency
            idx = idx+1;
            [dataOut(idx),validOut(idx)] = HDLCIC_vec( ...
                fi(zeros(vecSize,1),1,16,8), ...
                false);
        end
    end
end

Compare Function Output with Reference Data

Compare the function results against the output from the dsp.CICDecimator object.

cicOutput = dataOut(validOut==1);

fprintf('\nCIC Decimator\n');
difference = (abs(cicOutput-refOutput(1:length(cicOutput)))>0);
fprintf(['\nTotal number of samples differed between Behavioral ' ...
    'and HDL simulation: %d \n'],sum(difference));

CIC Decimator

Total number of samples differed between Behavioral and HDL simulation: 0 

Explore Latency of CIC Decimator Object

The latency of the dsphdl.CICDecimator System object™ varies depending on how many integrator and comb sections your filter has, the input vector size, and whether you enable gain correction. Use the getLatency function to find the latency of a particular filter configuration. The latency is the number of cycles between the first valid input and the first valid output, assuming the input is continuously valid.

Create a dsphdl.CICDecimator System object and request the latency. The default System object filter has two integrator and comb sections, and the gain correction is disabled.

hdlcic = dsphdl.CICDecimator

hdlcic = 
  dsphdl.CICDecimator with properties:

     DecimationSource: 'Property'
     DecimationFactor: 2
    DifferentialDelay: 1
          NumSections: 2
       GainCorrection: false

  Show all properties

L_def = getLatency(hdlcic)

L_def = 
5

Modify the filter object so it has three integrator and comb sections. Check the resulting change in latency.

hdlcic.NumSections = 3;
L_3sec = getLatency(hdlcic)

L_3sec = 
6

Enable the gain correction on the filter object with vector input size 2. Check the resulting change in latency.

hdlcic.GainCorrection = true;
vecSize = 2;
L_wgain = getLatency(hdlcic,vecSize)

L_wgain = 
25

Algorithms

CIC Decimation Filter

The transfer function of a CIC decimation filter is

$$H(z)={\left[{\displaystyle \sum _{k=0}^{RM-1}{z}^{-k}}\right]}^N=\frac{{\left(1-z^{-RM}\right)}^N}{{\left(1-z^{-1}\right)}^N}=\frac{1}{{\left(1-z^{-1}\right)}^N}·\frac{{\left(1-z^{-RM}\right)}^N}{1}=H_{\text{I}}{}^N(z)·H_{\text{c}}{}^N(z).$$

• H_I is the transfer function of the integrator part of the CIC filter.

• H_C is the transfer function of the comb part of the CIC filter.

• N is the number of sections. The number of sections in a CIC filter is defined as the number of sections in either the comb part or the integrator part of the filter. This value does not represent the total number of sections throughout the entire filter.

• R is the decimation factor.

• M is the differential delay.

CIC Filter Structure

The dsphdl.CICDecimator System object has the CIC filter structure shown in this figure. The structure consists of N sections of cascaded integrators, a rate change factor of R, and N sections of cascaded comb filters [1].

Designs can put the unit delay in the integrator part of the CIC filter in either the feedforward or feedback path. These two configurations yield an identical filter frequency response. However, the numerical outputs from these two configurations are different due to the latency of the paths. This System object puts the unit delay in the feedforward path of the integrator.

Fixed and Variable Decimation

The System object downsamples the integrator stage output using R, either based on the fixed decimation rate provided using the DecimationFactor property or the variable decimation rate provided using the R input argument. At the downsampler stage, the System object uses a counter to count the valid input samples, which depend on the decimation rate. Whenever the decimation rate changes, the object resets and starts a new calculation from the next sample. This mechanism prevents the System object from accumulating invalid values. Then, the System object provides the decimated output to the comb part.

Gain Correction

The gain of the System object is given by $$Gain={(R\text{x}M)}^N$$.

• R is the DecimationFactor property value.

• M is the DifferentialDelay property value.

• N is the NumSections property value.

The System object implements gain correction in two parts: coarse gain and fine gain. In coarse gain correction, the System object calculates the shift value, adds the shift value to the fractional bits to create a numeric type, and then performs a bit-shift left. In fine gain correction, the System object divides the remaining gain with the coarse gain if the gain is not a power of 2 and then multiplies the coarse gain corrected value with the inverse value of fine gain. All possible shift and fine gain values are precalculated and stored in an array before the System object starts processing.

You can modify this equation as $$Gain=2^{cGain}\text{x}fGain$$, where cGain means coarse gain and fGain means fine gain.

• $$cGain=floor({\log }_{2}Gain)$$

• $$fGain=Gain/2^{cGain}=Gain\text{x}{2}^{-cGain}{}^{}$$

To perform GainCorrection when the InterpolationSource property is set to 'Input port', the System object sets the output data type configured with the maximum decimation rate and bit-shifts left for all the values under the maximum decimation rate. The bit-shift value is equal to $$Maximumgain-{\log }_2(currentgain)$$.

Output Data Type

This section explains how the System object determines the output data type. For example, consider a filter with DecimationFactor, DifferentialDelay, and NumSections values of 8, 1, and 3, respectively, with an input width of 16 bits.

The output word length is calculated as $$B_{\text{Out}}=B_{\text{In}}+[{\log }_2(Gain)]$$.

• $$Gain={(R\text{x}M)}^N$$

• B_In is the input word length.

• B_Out is the output word length.

When you set the OutputDataType property to 'Full precision', the System object returns data with a word length of 25 bits, by adding nine gain bits to the input word length.

When you set the OutputDataType property to 'Same word length as input', the object outputs data with a word length of 16, which is the same length as the input word length. The internal integrator and comb stages use the full-precision data type with 25 bits.

When you set the OutputDataType property to 'Minimum section word lengths' and the OutputWordLength property to 16, the System object returns data with a word length of 16 bits. In this case, the object changes the bit width at each stage, based on the pruning algorithm.

If the OutputWordLength property value is less than the number of bits requested at the output, the least significant bits (LSBs) at the earlier stages are pruned. The Hogenauer algorithm provides the number of LSBs to discard at each stage. This algorithm minimizes the loss of information in the output data [1].

Latency

The latency of the System object varies depending on the type of input, the decimation you specify, the number of sections, and the value of the GainCorrection property. This table shows the latency of the System object. N is the number of sections and vecLen is the length of the vector.

Input Data	Output Data	Decimation Type	Gain Correction	Latency in Clock Cycles
Scalar	Scalar	Fixed	off	3 + N. When R = 1, 2 + N.
			on	3 + N + 9. When R = 1, 2 + N + 9.
Scalar	Scalar	Variable	off	4 + N. When Rmax = 1, 3 + N.
			on	4 + N + 9. When Rmax = 1, 3 + N + 9.
Vector	Scalar	Fixed	off	floor((vecLen – 1) x (N/vecLen)) + 1 + N + (2 + (vecLen + 1) x N
			on	floor((vecLen – 1) x (N/vecLen)) + 1 + N + (2 + (vecLen + 1) x N) + 9
Vector	Vector	Fixed	off	floor((vecLen – 1) x (N/vecLen)) + 1 + N + (2 + (vecLen + 1) x N
			on	floor((vecLen – 1) x (N/vecLen)) + 1 + N + (2 + (vecLen + 1) x N) + 9

Note

For vector inputs, the System object does not support variable decimation.

Scalar Input

This section shows the output of the System object for a scalar input with different R, M, and N values.

This figure shows the output of the System object with the default configuration, that is, with a fixed decimation rate and DecimationFactor, DifferentialDelay, and NumSections values of 2, 1, and 2, respectively. The System object returns valid output data at every second cycle based on the fixed DecimationFactor value of 2. The latency of the System object is 5 clock cycles, calculated as 3 + N.

This figure shows the output of the System object with a fixed decimation rate, DecimationFactor, DifferentialDelay, and NumSections values of 8, 1, and 3, respectively, and GainCorrection set to true. The System object returns valid output data at every eighth cycle based on the fixed DecimationFactor value of 8. The latency of the object is 15 clock cycles and is calculated as 3 + N + 9.

This figure shows the output of the System object for variable R values of 2, 4, and 8 along with M and N values of 1 and 3. The GainCorrection property is set to false. The System object returns valid output data at the second, fourth, and eighth cycles corresponding to the R values 2, 4, and 8, respectively. The System object accepts R argument value changes only when the input validIn is 1 (true). The latency of the System object is 7 clock cycles, calculated as 4 + N.

Vector Input

This section shows the output of the System object for a vector input with different R, M, and N values.

This figure shows the output of the System object for a two-element column vector input with the default configuration, that is, with a fixed decimation rate and DecimationFactor, DifferentialDelay, and NumSections values of 2, 1, and 2, respectively. The latency of the object is 12 clock cycles.

This figure shows the output of the System object for an eight-element column vector input with a fixed decimation rate, R, M, and N values of 8, 1, and 3, respectively, and GainCorrection set to true. The latency of the object is 44 clock cycles.

Performance

The performance of the synthesized HDL code varies with your target and synthesis options. It also varies based on the input data type.

This table shows the resource and performance data synthesis results of the object for a scalar input of type fixdt(1,16,0) with fixed and variable decimation rates and for a two-element column vector input with fixed decimation rate DecimationFactor, DifferentialDelay, and NumSections values are 2, 1, and 2, respectively. The generated HDL is targeted to the AMD^® Zynq^®-7000 ZC706 Evaluation Board.

Input Data	Decimation Type	Slice LUTs	Slice Registers	Maximum Frequency in MHz
Scalar	Fixed rate	101	166	711.74
	Variable rate	206	186	441.70
Vector	Fixed rate	218	627	624.61

The resources and frequencies vary based on the type of input data and the values of R, M, and N, as well as other properties. Using a vector input can increase the throughput, however, doing so also increases the number of hardware resources that the System object uses.

References

[1] Hogenauer, E. “An Economical Class of Digital Filters for Decimation and Interpolation.” IEEE Transactions on Acoustics, Speech, and Signal Processing 29, no. 2 (April 1981): 155–62. https://doi.org/10.1109/TASSP.1981.1163535.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

This System object supports C/C++ code generation for accelerating MATLAB simulations, and for DPI component generation.

HDL Code Generation

Generate VHDL, Verilog and SystemVerilog code for FPGA and ASIC designs using HDL Coder™.

The software supports double and single data types for simulation, but not for HDL code generation.

To generate HDL code from predefined System objects, see Generate HDL Code for IIR Filter.

Version History

Introduced in R2019b

R2022a: Moved to DSP HDL Toolbox from DSP System Toolbox

Before R2022a, this System object was named dsp.HDLCICDecimation and was included in the DSP System Toolbox™.

R2022a: Changes to decimation factor arguments

• You can now set the decimation factor to 1. In previous releases, a decimation factor of 1 was invalid.

• The ResetIn property is renamed to ResetInputPort.

Configuration	Before R2022a	After 2022a
Variable decimation factor	Select the VariableDownsample property and set the DecimationFactor parameter to the maximum expected decimation factor.	Set the DecimationSource property to 'Input port' and set the MaxDecimationFactor property to the maximum expected decimation factor. The decimFactor argument is renamed to R.
Fixed decimation factor	Clear the VariableDownsample property and set the DecimationFactor property to the desired decimation factor.	Set the DecimationSource property to 'Property' and set the DecimationFactor property to the desired decimation factor.

R2021b: High-throughput interface

The object accepts and returns a column vector of elements that represent samples in time. The input vector can contain up to 64 samples. When you use frame-based input, you must use a fixed decimation factor.

R2020a: Gain correction and programmable decimation factor

You can optionally enable automatic gain correction. You can also specify the decimation factor as an input argument.