dsp.CICDecimator

Decimate signal using cascaded integrator-comb (CIC) filter

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Description

Thedsp.CICDecimatorSystem object™ decimates an input signal using a cascaded integrator-comb (CIC) decimation filter. The CIC decimation filter structure consists ofNsections of cascaded integrators, followed by a rate change by a factor ofR, followed byNsections of cascaded comb filters. For details, seeAlgorithms. TheNumSectionsproperty specifiesN,number of sections in the CIC filter. TheDecimationFactorproperty specifiesR,decimation factor. ThegetFixedPointInfofunction returns the word lengths and fraction lengths of the fixed-point sections and the output for thedsp.CICDecimatorSystem object. You can also generate HDL code for this System object using thegeneratehdlfunction.

Note

This object requires a Fixed-Point Designer™ license.

To decimate a signal using a CIC filter:

Create thedsp.CICDecimatorobject and set its properties.
Call the object with arguments, as if it were a function.

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

Creation

Syntax

cicDecim = dsp.CICDecimator

cicDecim = dsp.CICDecimator(R,M,N)

cicDecim = dsp.CICDecimator(Name,Value)

Description

example

cicDecim= dsp.CICDecimatorcreates a CIC decimation System object that applies a CIC decimation filter to the input signal.

example

cicDecim= dsp.CICDecimator(R,M,N)creates a CIC decimation object with theDecimationFactorproperty set toR,DifferentialDelayproperty set toM, and theNumSectionsproperty set toN.

cicDecim= dsp.CICDecimator(Name,Value)creates a CIC decimation object with each specified property set to the specified value. Enclose each property name in single quotes. You can use this syntax with any previous input argument combination.

Properties

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

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

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

`DecimationFactor`—Decimation factor
`2`(default) |positive integer

Factor by which the input signal is decimated, specified as a positive integer.

`DifferentialDelay`—Differential delay of filter comb sections
`1`(default) |positive integer

Differential delay value used in each of the comb sections of the filter, specified as a positive integer. For details, seeAlgorithms. If the differential delay is a built-in integer data type, the decimation factor must be the same integer data type ordouble. For example, if the differential delay is anint8,n the decimation factor must be anint8ordouble.

`NumSections`—Number of integrator and comb sections
`2`(default) |positive integer

Number of integrator and comb sections of the CIC filter, specified as a positive integer. This number indicates the number of sections in either the comb part or the integrator part of the filter. The total number of sections in the CIC filter is twice the number of sections given by this property.

`FixedPointDataType`—Fixed-point property designations
`Full precision`(default) |`Minimum section word lengths`|`Specify word lengths`|`Specify word and fraction lengths`

Fixed-point property designations, specified as one of the following:

Full precision– The word length and fraction length of the CIC filter sections and the object output operate in full precision.
Minimum section word lengths– Specify the output word length through theOutputWordLengthproperty. The object determines the filter section data type and the output fraction length that give the best possible precision. For details, seegetFixedPointInfoandcicDecimOutargument.
Specify word lengths– Specify the word lengths of the CIC filter sections and the object output through theSectionWordLengthsandOutputWordLengthproperties. The object determines the corresponding fraction lengths to give the best possible precision. For details, seegetFixedPointInfoand thecicDecimOutargument.
Specify word and fraction lengths– Specify the word length and fraction length of the CIC filter sections and the object output through theSectionWordLengths,SectionFractionLengths,OutputWordLength, andOutputFractionLengthproperties.

`SectionWordLengths`—Fixed-point word lengths for each filter section
`[16 16 16 16]`(default) |scalar|vector

Fixed-point word lengths to use for each filter section, specified as a scalar or a row vector of integers. The word length must be greater than or equal to 2. If you specify a scalar, the value applies to all the sections of the filter. If you specify a vector, the vector must be of length 2 ×NumSections.

Example:32

Example:[32 32 32 32]

Dependencies

This property applies when you set theFixedPointDataTypeproperty to'Specify word lengths'or'Specify word and fraction lengths'.

`SectionFractionLengths`—Fixed-point fraction lengths for each filter section
`0`(default) |scalar|vector

Fixed-point fraction lengths to use for each filter section, specified as a scalar or a row vector of integers. The fraction length can be negative, 0, or positive. If you specify a scalar, the value applies to all the sections of the filter. If you specify a vector, the vector must be of length 2 ×NumSections.

Example:-2

Example:[-2 0 5 8]

Dependencies

This property applies when you set theFixedPointDataTypeproperty to'Specify word and fraction lengths'.

`OutputWordLength`—Fixed-point word length for filter output
`32`(default) |scalar integer

Fixed-point word length to use for the filter output, specified as a scalar integer greater than or equal to 2.

Dependencies

This property applies when you set theFixedPointDataTypeproperty to'Minimum section word lengths','Specify word lengths', or'Specify word and fraction lengths'.

`OutputFractionLength`—Fixed-point fraction length for filter output
`0`(default) |scalar integer

Fixed-point fraction length to use for the filter output, specified as a scalar integer.

Dependencies

This property applies when you setFixedPointDataTypeproperty to'Specify word and fraction lengths'.

Usage

Syntax

cicDecimOut = cicDecim(input)

Description

example

cicDecimOut= cicDecim(input)decimates the input using a CIC decimator.

Input Arguments

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`input`—Data input
vector|matrix

Data input, specified as a vector or matrix. The number of rows in the input must be a multiple of theDecimationFactor. If the input is ofsingleordoubledata type, property settings related to the fixed-point data types are ignored.

Output Arguments

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`cicDecimOut`— CIC decimator output
vector | matrix

Decimated output, returned as a vector or a matrix. The output frame size equals (1 ∕DecimationFactor)×输入帧大小。输出的复杂性data matches that of the input data. If the input issingleordouble,output data type matches the input data type.

If the input is of built-in integer data type or of fixed-point data type, the output word length and fraction length depend on the fixed-point data type setting you choose through theFixedPointDataTypeproperty.

Full precision

When theFixedPointDataTypeis set to'Full precision',following relationship applies:

$\begin{array}{l} W L_{output} = W L_{input} + N u m S e c t \\ F L_{output} = F L_{input} \end{array}$

where,

WL_output–– Word length of the output data.
FL_output–– Fraction length of the output data.
WL_input–– Word length of the input data.
FL_input–– Fraction length of the input data.
NumSect–– Number of sections in the CIC filter specified through theNumSectionsproperty.

TheWL_inputandFL_inputare inherited from the data input you pass to the object algorithm. For built-in integer inputs, the fraction length is 0.

Minimum section word lengths

When theFixedPointDataTypeproperty is set to'Minimum section word lengths',output word length is the value you specify in theOutputWordLengthproperty. The output fraction length,FL_output, is given by:

$F L_{output} = W L_{output} - (W L_{input} - F L_{input} + N u m S e c t)$

Specify word and fraction lengths

When theFixedPointDataTypeproperty is set to'Specify word and fraction lengths',output word length and fraction length are the values you specify in theOutputWordLengthandOutputFractionLengthproperties.

Specify word lengths

When theFixedPointDataTypeproperty is set to'Specify word lengths',output word length is the value you specify in theOutputWordLengthproperty. The output fraction length,FL_output, is given by:

$F L_{output} = W L_{output} - (W L_{input} - F L_{input} + N u m S e c t)$

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 namedobj, use this syntax:

release(obj)

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Specific to dsp.CICDecimator

`generatehdl`	Generate HDL code for quantized DSP filter (requiresFilter Design HDL Coder)
`impz`	Impulse response of discrete-time filterSystem object
`freqz`	Frequency response of discrete-time filterSystem object
`phasez`	Phase response of discrete-time filterSystem object(unwrapped)
`fvtool`	Visualize frequency response of DSP filters
`gain`	Gain of CIC filterSystem object
`getFixedPointInfo`	Get fixed-point word and fraction lengths
`info`	Information about filterSystem object

Common to All System Objects

`step`	RunSystem objectalgorithm
`release`	Release resources and allow changes toSystem objectproperty values and input characteristics
`reset`	Reset internal states ofSystem object

For a list of filter analysis methods this object supports, typedsp.CICDecimator.helpFilterAnalysisin the MATLAB^®command prompt. For the corresponding function reference pages, seeAnalysis Methods for Filter System Objects.

Examples

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使用CICDecimator毁掉一个信号Object

Open Live Script

Note: If you are using R2016a or an earlier release, replace each call to the object with the equivalent step syntax. For example,obj(x)becomesstep(obj,x).

Create adsp.CICDecimatorSystem object™ withDecimationFactorset to 4. Decimate a signal from 44.1 kHz to 11.025 kHz.

cicdec = dsp.CICDecimator(4); cicdec.FixedPointDataType ='Minimum section word lengths'; cicdec.OutputWordLength = 16;

Create a fixed-point sinusoidal input signal of 1024 samples, with a sampling frequency of 44.1e3 Hz.

Fs = 44.1e3;% 0.0232 sec signaln = (0:1023)'; x = fi(sin(2*pi*1e3/Fs*n),true,16,15);

Create adsp.SignalSourceobject.

src = dsp.SignalSource(x,64);

Decimate the output with 16 samples per frame.

y = zeros(16,16);forii = 1:16 y(ii,:) = cicdec(src());end

Plot the first frame of the original and decimated signals. Output latency is 2 samples.

D = cicdec.DecimationFactor; diffDelay = cicdec.DifferentialDelay; NumSect = cicdec.NumSections; gainCIC =...(D*diffDelay)^NumSect; stem(n(1:56)/Fs,double(x(4:59))) holdon; stem(n(1:14)/(Fs/D),double(y(1,3:end))/gainCIC,...'r','filled') xlabel('Time (sec)') ylabel('Signal Amplitude') legend('Original signal',...'Decimated signal',...“位置”,'north') holdoff;

Figure contains an axes object. The axes object contains 2 objects of type stem. These objects represent Original signal, Decimated signal.

Using theinfomethod in'long'format, obtain the word lengths and fraction lengths of the fixed-point filter sections and the filter output.

info(cicdec,'long')

ans = 'Discrete-Time FIR Multirate Filter (real) ----------------------------------------- Filter Structure : Cascaded Integrator-Comb Decimator Decimation Factor : 4 Differential Delay : 1 Number of Sections : 2 Stable : Yes Linear Phase : Yes (Type 1) Implementation Cost Number of Multipliers : 0 Number of Adders : 4 Number of States : 4 Multiplications per Input Sample : 0 Additions per Input Sample : 2.5 Fixed-Point Info Section word lengths : 20 19 19 18 Section fraction lengths : 15 14 14 13 Output word length : 16 Output fraction length : 11 '

Determine the Section and Output Word Lengths and Fraction Lengths

Open Live Script

Using thegetFixedPointInfofunction, you can determine the word lengths and fraction lengths of the fixed-point sections and the output of thedsp.CICDecimatoranddsp.CICInterpolatorSystem objects. The data types of the filter sections and the output depend on theFixedPointDataTypeproperty of the filter System object™.

Full precision

Create adsp.CICDecimatorobject. The default value of theNumSections房地产是2。此值表示two integrator and comb sections. The WLs and FLs vectors returned by thegetFixedPointInfofunction contain five elements each. The first two elements represent the two integrator sections. The third and fourth elements represent the two comb sections. The last element represents the filter output.

cicD = dsp.CICDecimator

cicD = dsp.CICDecimator with properties: DecimationFactor: 2 DifferentialDelay: 1 NumSections: 2 FixedPointDataType: 'Full precision'

By default, theFixedPointDataTypeproperty of the object is set to'Full precision'. Calling thegetFixedPointInfofunction on this object with the input numeric type,nt, yields the following word length and fraction length vectors.

nt = numerictype(1,16,15)

nt = DataTypeMode: Fixed-point: binary point scaling Signedness: Signed WordLength: 16 FractionLength: 15

[WLs,FLs] = getFixedPointInfo(cicD,nt)%#ok

WLs =1×518 18 18 18 18

FLs =1×515 15 15 15 15

For details on how the word lengths and fraction lengths are computed, see the description forOutput Arguments.

If you lock thecicDobject by passing an input to its algorithm, you do not need to pass thentargument to thegetFixedPointInfofunction.

input = int64(randn(8,1))

input =8x1 int64 column vector1 2 -2 1 0 -1 0 0

output = cicD(input)

output = 0 1 3 0 DataTypeMode: Fixed-point: binary point scaling Signedness: Signed WordLength: 66 FractionLength: 0

[WLs,FLs] = getFixedPointInfo(cicD)%#ok

WLs =1×566 66 66 66 66

FLs =1×50 0 0 0 0

The output and section word lengths are the sum of input word length, 64 in this case, and the number of sections, 2. The output and section fraction lengths are 0 since the input is a built-in integer.

Minimum section word lengths

Release the object and change theFixedPointDataTypeproperty to'Minimum section word lengths'. Determine the section and output fixed-point information when the input is fixed-point data,fi(randn(8,2),1,24,15).

release(cicD); cicD.FixedPointDataType ='Minimum section word lengths'

cicD = dsp.CICDecimator with properties: DecimationFactor: 2 DifferentialDelay: 1 NumSections: 2 FixedPointDataType: 'Minimum section word lengths' OutputWordLength: 32

inputF = fi(randn(8,2),1,24,15)

inputF = 3.5784 -0.1241 2.7694 1.4897 -1.3499 1.4090 3.0349 1.4172 0.7254 0.6715 -0.0630 -1.2075 0.7148 0.7172 -0.2050 1.6302 DataTypeMode: Fixed-point: binary point scaling Signedness: Signed WordLength: 24 FractionLength: 15

[WLs, FLs] = getFixedPointInfo(cicD,numerictype(inputF))%#ok

WLs =1×526 26 26 26 32

FLs =1×515 15 15 15 21

Specify word and fraction lengths

Change theFixedPointDataTypeproperty to'Specify word and fraction lengths'. Determine the fixed-point information using thegetFixedPointInfofunction.

cicD.FixedPointDataType ='Specify word and fraction lengths'

cicD = dsp.CICDecimator with properties: DecimationFactor: 2 DifferentialDelay: 1 NumSections: 2 FixedPointDataType: 'Specify word and fraction lengths' SectionWordLengths: [16 16 16 16] SectionFractionLengths: 0 OutputWordLength: 32 OutputFractionLength: 0

[WLs, FLs] = getFixedPointInfo(cicD,numerictype(inputF))%#ok

WLs =1×516 16 16 16 32

FLs =1×50 0 0 0 0

The section and output word lengths and fraction lengths are assigned as per the respective fixed-point properties of thecicDobject. These values are not determined by the input numeric type. To confirm, call thegetFixedPointInfofunction without passing thenumerictypeinput argument.

[WLs, FLs] = getFixedPointInfo(cicD)%#ok

WLs =1×516 16 16 16 32

FLs =1×50 0 0 0 0

Specify word lengths

To specify the word lengths of the filter section and output, set theFixedPointDataTypeproperty to'Specify word lengths'.

cicD.FixedPointDataType ='Specify word lengths'

cicD = dsp.CICDecimator with properties: DecimationFactor: 2 DifferentialDelay: 1 NumSections: 2 FixedPointDataType: 'Specify word lengths' SectionWordLengths: [16 16 16 16] OutputWordLength: 32

ThegetFixedPointInfofunction requires the input numeric type because that information is used to compute the section and word fraction lengths.

[WLs, FLs] = getFixedPointInfo(cicD,numerictype(inputF))

WLs =1×516 16 16 16 32

FLs =1×55 5 5 5 21

For more details on how the function computes the word and fraction lengths, see the description forOutput Arguments.

More About

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CIC Filter

CIC filters are an optimized class of linear phase FIR filters composed of a comb part and an integrator part.

The CIC decimation filter is conceptually given by a single rate CIC filter,H(z)which is a lowpass anti-imaging filter, followed by a downsampler. The CIC decimation filter decreases the sample rate of an input signal by an integer factor using a cascaded integrator-comb (CIC) filter.

In a more efficient implementation, the single rate CIC filterH(z)is factorized this way:

$H (z) = {[\sum_{k = 0}^{R M - 1} z^{- k}]}^{N} = \frac{{(1 - z^{- R M})}^{N}}{{(1 - z^{- 1})}^{N}} = \frac{1}{{(1 - z^{- 1})}^{N}} \cdot \frac{{(1 - z^{- R M})}^{N}}{1} = H_{I}^{N} (z) \cdot H_{c}^{N} (z)$

where,

H_Iis the transfer function of the integrator part of the filter containingNstages of integrators.
H_Cis the transfer function of theNsections of the cascaded comb filters, each with a width ofRM.
Nis the number of sections. The number of sections in a CIC filter is defined as the number of sections in either the comb partorthe integrator part of the filter. This value does not represent the total number of sections throughout the entire filter.
Ris the decimation factor.
Mis the differential delay.

In the overall multirate realization, the algorithm applies the noble identity for decimation and moves the rate change factor,R, to follow after theNsections of the cascaded integrators. The transfer function of the resulting filter is given by the following equation:

$H (z) = \frac{{(1 - z^{- M})}^{N}}{{(1 - z^{- 1})}^{N}} .$

For a block diagram that shows the multirate implementation, seeAlgorithms.

Fixed Point

The fixed-point signal diagram shows the data types that thedsp.CICDecimatorobject uses for fixed-point signals.

where,

secNT = numerictype(1,secWL,secFL)
outNT = numertictype(1,outWL,outFL)
secWLis the section word length you specify through theSectionWordLengthsproperty.
secFLis the section fraction length you specify through theSectionFractionLengthsproperty.
outWLis the output word length you specify through theOutputWordLengthproperty.
outFLis the output fraction length you specify through theOutputFractionLengthproperty.

The value ofNumSectionsin this diagram is 2.

Algorithms

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CIC Decimation Filter

The CIC decimation filter inMore Aboutis realized as a cascade ofNsections of the integrators followed by a rate change factor ofR, followed byNsections of comb filters.

This diagram shows two sections of cascaded integrators and two sections of cascaded comb filters. The unit delay in the integrator portion of the CIC filter can be located in either the feedforward or the feedback path. These two configurations yield identical filter frequency response. However, the numerical outputs from these two configurations are different due to the latency. This block puts the unit delay in the feedforward path of the integrator because it is a preferred configuration for HDL implementation.

References

[1] Hogenauer, E.B. "An Economical Class of Digital Filters for Decimation and Interpolation."IEEE Transactions on Acoustics, Speech and Signal Processing. Volume 29, Number 2, 1981, 155–162.

[2] Meyer-Baese, U.Digital Signal Processing with Field Programmable Gate Arrays. New York: Springer, 2001.

[3] Harris, Fredric J.Multirate Signal Processing for Communication Systems. Indianapolis, IN: Prentice Hall PTR, 2004.

Extended Capabilities

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

Usage notes and limitations:

SeeSystem Objects in MATLAB Code Generation(MATLAB Coder).

HDL Code Generation
Generate Verilog and VHDL code for FPGA and ASIC designs using HDL Coder™.

This object supports HDL code generation with the Filter Design HDL Coder™ product. For workflows and limitations, seeGenerate HDL Code for Filter System Objects(Filter Design HDL Coder).

Version History

Introduced in R2012a

dsp.CICDecimator

Description

Creation

Syntax

Description

Properties

DecimationFactor—Decimation factor2(default) |positive integer

DifferentialDelay—Differential delay of filter comb sections1(default) |positive integer

NumSections—Number of integrator and comb sections2(default) |positive integer

FixedPointDataType—Fixed-point property designationsFull precision(default) |Minimum section word lengths|Specify word lengths|Specify word and fraction lengths

SectionWordLengths—Fixed-point word lengths for each filter section[16 16 16 16](default) |scalar|vector

Dependencies

SectionFractionLengths—Fixed-point fraction lengths for each filter section0(default) |scalar|vector

Dependencies

OutputWordLength—Fixed-point word length for filter output32(default) |scalar integer

Dependencies

OutputFractionLength—Fixed-point fraction length for filter output0(default) |scalar integer

Dependencies

Usage

Syntax

Description

Input Arguments

input—Data inputvector|matrix

Output Arguments

cicDecimOut— CIC decimator outputvector | matrix

Object Functions

Specific to dsp.CICDecimator

Common to All System Objects

Examples

使用CICDecimator毁掉一个信号Object

Determine the Section and Output Word Lengths and Fraction Lengths

More About

CIC Filter

Fixed Point

Algorithms

CIC Decimation Filter

References

Extended Capabilities

C/C++ Code GenerationGenerate C and C++ code using MATLAB® Coder™.

HDL Code GenerationGenerate Verilog and VHDL code for FPGA and ASIC designs using HDL Coder™.

Version History

See Also

Functions

Objects

Blocks

Topics

`DecimationFactor`—Decimation factor
`2`(default) |positive integer

`DifferentialDelay`—Differential delay of filter comb sections
`1`(default) |positive integer

`NumSections`—Number of integrator and comb sections
`2`(default) |positive integer

`FixedPointDataType`—Fixed-point property designations
`Full precision`(default) |`Minimum section word lengths`|`Specify word lengths`|`Specify word and fraction lengths`

`SectionWordLengths`—Fixed-point word lengths for each filter section
`[16 16 16 16]`(default) |scalar|vector

`SectionFractionLengths`—Fixed-point fraction lengths for each filter section
`0`(default) |scalar|vector

`OutputWordLength`—Fixed-point word length for filter output
`32`(default) |scalar integer

`OutputFractionLength`—Fixed-point fraction length for filter output
`0`(default) |scalar integer

`input`—Data input
vector|matrix

`cicDecimOut`— CIC decimator output
vector | matrix

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

HDL Code Generation
Generate Verilog and VHDL code for FPGA and ASIC designs using HDL Coder™.