dsp。CICInterpolator

Interpolate signal using cascaded integrator-comb filter

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Description

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

Note

This object requires a Fixed-Point Designer™ license.

To interpolate a signal using a CIC filter:

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

了解更多关于系统对象是如何工作的,看到的What Are System Objects?.

Creation

Syntax

cicInterp = dsp.CICInterpolator

cicInterp = dsp.CICInterpolator(R,M,N)

cicInterp = dsp.CICInterpolator(Name,Value)

Description

example

cicInterp= dsp.CICInterpolatorcreates a CIC interpolation System object that applies a CIC interpolation filter to the input signal.

example

cicInterp= dsp.CICInterpolator(R,M,N）creates a CIC interpolation object with theInterpolationFactorproperty set toR,DifferentialDelayproperty set toM, and theNumSectionsproperty set toN.

cicInterp= dsp.CICInterpolator(Name,Value）creates a CIC interpolation 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 combinations.

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.

`InterpolationFactor`—Interpolation factor
`2`(default) |positive integer

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

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

延迟微分值用于每一个梳子sections of the filter, specified as a positive integer. For details, seeAlgorithms. If the differential delay is of built-in integer class data type, the interpolation factor must be the same integer data type ordouble. For example, if the differential delay is anint8,n the interpolation 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, seegetFixedPointInfoandcicInterpOutargument.
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 thecicInterpOutargument.
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]

依赖关系

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]

依赖关系

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.

依赖关系

This property applies when you set theFixedPointDataTypeproperty to one of'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.

依赖关系

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

Usage

Syntax

cicInterpOut = cicInterp(input)

Description

example

cicInterpOut= cicInterp(input)interpolates the input using a CIC interpolator.

Input Arguments

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`input`—Data input
vector|matrix

数据输入,指定为一个向量或矩阵。如果the input is of single or double data type, property settings related to the fixed-point data types are ignored.

Output Arguments

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`cicInterpOut`— CIC interpolator output
vector | matrix

Interpolated output, returned as a vector or a matrix. The output frame size equals (InterpolationFactor）× input frame size. The complexity of the output data matches that of the input data. If the input issingleordouble,output data type matches the input data type.

如果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 theFixedPointDataTypeproperty is 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.

WL_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 inOutputWordLengthproperty. The output fraction length,FL_outputis given by the following equation:

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

Specify word and fraction lengths

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

Specify word lengths

When theFixedPointDataTypeis set to'Specify word lengths',output word length is the value you specify in theOutputWordLengthproperty. The output fraction length,FL_outputis given by the following equation:

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

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.CICInterpolator

`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。CICInterpolator.helpFilterAnalysisin the MATLAB^®command prompt. For the corresponding function reference pages, seeAnalysis Methods for Filter System Objects.

Examples

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Interpolate Signal Using CICInterpolator System object

Open Live Script

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

Create adsp。CICInterpolatorSystem object™ withInterpolationFactorset to 2. Interpolate a fixed-point signal by a factor of 2 from 22.05 kHz to 44.1 kHz.

cicint = dsp。CICInterpolator(2)

cicint = dsp。CICInterpolator with properties: InterpolationFactor: 2 DifferentialDelay: 1 NumSections: 2 FixedPointDataType: 'Full precision'

Create adsp。SineWaveobject withSampleRateset to 22.05 kHz,SamplesPerFrameset to 32, andOutputDataTypeset to'Custom'. To generate a fixed-point signal, set theCustomOutputDataTypeproperty to anumerictypeobject. For the purpose of this example, set the value tonumerictype([],16). The fraction length is computed based on the values of the generated sinusoidal signal to give the best possible precision.

To generate a fixed-point signal, set theMethodproperty of thedsp。SineWaveobject to'Table lookup'. This method of generating the sinusoidal signal requires that the period of every sinusoid in the output be evenly divisible by the sample period. That is, $1 / f_{i} T_{s} = k_{i}$ must be an integer value for every channeli= 1, 2, ...,N.The value of $T_{s}$ equals $1 / F_{s}$ ,variable $f_{i}$ is the frequency of the sinusoidal signal, and $F_{s}$ is the sample rate of the signal. In other words, the ratio $F_{s} / f_{i}$ must be an integer. For more details, see theAlgorithmssection on thedsp。SineWaveobject page.

In this example, $F_{s}$ is set to 22050 Hz and $f_{i}$ is set to 1050 Hz.

Fs = 22.05e3; sine = dsp.SineWave('Frequency',1050,'SampleRate',Fs,'SamplesPerFrame',32,...'Method','Table lookup','OutputDataType','Custom'）

sine = dsp.SineWave with properties: Amplitude: 1 Frequency: 1050 PhaseOffset: 0 ComplexOutput: false Method: 'Table lookup' TableOptimization: 'Speed' SampleRate: 22050 SamplesPerFrame: 32 OutputDataType: 'Custom' Show all properties

In each loop of the iteration, stream in a frame of the fixed-point sinusoidal signal sampled at 22.05 kHz. Interpolate the streamed signal by a factor of 2. The interpolated output has 64 samples per frame.

fori = 1:16 x = sine(); y = cicint(x);end

The output of the CIC interpolation filter is amplified by a specific gain value. You can determine this value using thegainfunction. This gain equals the gain of the $2 N^{th}$ stage of the CIC interpolation filter and equals ${(I \times D ）}^{N} / I$ , where $I$ is the interpolation factor, $D$ is the differential delay, and $N$ is the number of sections of the CIC interpolator.

gainCIC = gain(cicint)

gainCIC = 2

To adjust this amplified output and to match it to the amplitude of the original signal, divide the CIC interpolated signal with the computed gain value.

Compare the last frames of the original and the interpolated signals. While plotting, account for the output latency of 2 samples.

n = (0:63)'; stem(n(1:31)/Fs, double(x(1:31)),'r','filled'）holdon; I = cicint.InterpolationFactor; stem(n(1:61)/(Fs*I),...double(y(4:end))/gainCIC,'b'）xlabel('Time (sec)'）ylabel('Signal Amplitude'）legend('Original Signal','Interpolated Signal',...'location','north'）holdoff;

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

info(cicint,'long'）

ans = 'Discrete-Time FIR Multirate Filter (real) ----------------------------------------- Filter Structure : Cascaded Integrator-Comb Interpolator Interpolation Factor : 2 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 : 6 Fixed-Point Info Section word lengths : 17 17 17 17 Section fraction lengths : 14 14 14 14 Output word length : 17 Output fraction length : 14 '

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 theNumSectionsproperty is 2. This value indicates that there are 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=4×1 object0 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=8×2 object3.5784 -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

The CIC interpolation filter increases the sample rate of an input signal by an integer factor using a cascaded integrator-comb (CIC) filter.

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

The transfer function of the single rate CIC filterH(z)is given by the following equation:

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

where,

H_Cis the transfer function of the comb part of the filter.
H_Iis the transfer function of the integrator part of the filter.
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 interpolation factor.
Mis the differential delay.

For the multirate implementation, the algorithm applies the noble identity for interpolation and moves the rate change factor,R, to follow after theNsections of the cascaded comb filters. 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.

Algorithms

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CIC Interpolation Filter

The filterH(z)inMore Aboutis realized as an interpolation filter whenNsections of cascaded comb filters are followed by a rate change by a factorR, followed byNsections of cascaded integrators.

This diagram shows two sections of cascaded comb filters and two sections of cascaded integrators. 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 since 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).

Fixed-Point Conversion
Design and simulate fixed-point systems using Fixed-Point Designer™.

The fixed-point signal diagram shows the data types that thedsp。CICInterpolatorobject 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.

dsp。CICInterpolator

Description

Creation

Syntax

Description

Properties

InterpolationFactor—Interpolation 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

依赖关系

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

依赖关系

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

依赖关系

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

依赖关系

Usage

Syntax

Description

Input Arguments

input—Data inputvector|matrix

Output Arguments

cicInterpOut— CIC interpolator outputvector | matrix

Object Functions

Specific to dsp.CICInterpolator

Common to All System Objects

Examples

Interpolate Signal Using CICInterpolator System object

Determine the Section and Output Word Lengths and Fraction Lengths

More About

CIC Filter

Algorithms

CIC Interpolation Filter

References

Extended Capabilities

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

Fixed-Point ConversionDesign and simulate fixed-point systems using Fixed-Point Designer™.

See Also

Functions

Objects

Blocks

Topics

DSP System Toolbox Documentation

万博1manbetx

Efficient Multirate Signal Processing in MATLAB

`InterpolationFactor`—Interpolation 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

`cicInterpOut`— CIC interpolator output
vector | matrix

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

Fixed-Point Conversion
Design and simulate fixed-point systems using Fixed-Point Designer™.