dsp.CICCompensationInterpolator

Compensate for CIC interpolation filter using FIR interpolator

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Description

You can compensate for the shortcomings of a CIC interpolator, namely its passband droop and wide transition region, by preceding it with a compensation interpolator. This System object™ lets you design and use such a filter.

To compensate for the shortcomings of a CIC filter using an FIR interpolator:

Create thedsp.CICCompensationInterpolatorobject 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

ciccompint = dsp.CICCompensationInterpolator

ciccompint = dsp.CICCompensationInterpolator(interp)

ciccompint = dsp.CICCompensationInterpolator(cic)

ciccompint = dsp.CICCompensationInterpolator(cic,interp)

ciccompint = dsp.CICCompensationInterpolator(___,Name,Value)

Description

ciccompint= dsp.CICCompensationInterpolatorreturns a System object,ciccompint, that applies an FIR interpolator to each channel of an input signal. Using the properties of the object, the interpolation filter can be designed to compensate for a subsequent CIC filter.

ciccompint= dsp.CICCompensationInterpolator(interp)returns a CIC compensation interpolator System object,ciccompint, with theInterpolationFactorproperty set tointerp.

ciccompint= dsp.CICCompensationInterpolator(cic)returns a CIC compensation interpolator System object,ciccompint, with theCICRateChangeFactor,CICNumSections, andCICDifferentialDelayproperties specified in thedsp.CICInterpolatorSystem objectcic.

ciccompint= dsp.CICCompensationInterpolator(cic,interp)returns a CIC compensation interpolator System object,ciccompint, with theCICRateChangeFactor,CICNumSections, andCICDifferentialDelayproperties specified in thedsp.CICInterpolatorSystem objectcic, and theInterpolationFactorproperty set tointerp.

example

ciccompint= dsp.CICCompensationInterpolator(___,Name,Value)returns a CIC compensation interpolator object with each specified property set to the specified value. Enclose each property name in 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.

`CICDifferentialDelay`—微分延迟compens的CIC滤波器ated
`1`(default) |positive integer scalar

Specify the differential delay of the CIC filter being compensated as a positive integer scalar.

`CICNumSections`—Number of sections of the CIC filter being compensated
`2`(default) |positive integer scalar

Specify the number of sections of the CIC filter being compensated as a positive integer scalar.

`CICRateChangeFactor`—Rate-change factor of the CIC filter being compensated
`2`(default) |positive integer scalar

Specify the rate-change factor of the CIC filter being compensated as a positive integer scalar. The default is 2.

`DesignForMinimumOrder`—Design filter of minimum order or of specified order
`true`(default) |`false`

Specify whether to design a filter of minimum order or a filter of specified order as a logical scalar. The default istrue, which corresponds to a filter of minimum order.

`FilterOrder`—Order of interpolation compensator filter
12(default) |positive integer scalar

Specify the order of the interpolation compensator filter as a positive integer scalar.

Dependencies

This property applies only when you set theDesignForMinimumOrderproperty tofalse.

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

Specify the interpolation factor of the compensator System object as a positive integer scalar.

`PassbandFrequency`—Passband edge frequency in hertz
`100000`(default) |positive real scalar

Specify the passband edge frequency as a positive real scalar expressed in hertz.PassbandFrequencymust be less thanF_s/2, whereF_sis the output sample rate.

`PassbandRipple`—Filter passband ripple in decibels
`0.1`(default) |positive real scalar

Specify the filter passband ripple as a positive real scalar expressed in decibels.

`SampleRate`—Input sample rate in hertz
`600000`(default) |positive real scalar

Specify the input sample rate as a positive real scalar expressed in hertz.

Data Types:single|double

`StopbandAttenuation`—Filter stopband attenuation in decibels
`60`(default) |positive real scalar

Specify the filter stopband attenuation as a positive real scalar expressed in decibels.

`StopbandFrequency`—Stopband edge frequency in hertz
`400000`(default) |positive real scalar

Specify the stopband edge frequency as a positive real scalar expressed in hertz.StopbandFrequencymust be less thanF_s/2, whereF_sis the output sample rate.

Fixed-Point Properties

`CoefficientsDataType`—Word and fraction lengths of coefficients
`numerictype(1,16)`(default) |`numerictype`object

Word and fraction lengths of coefficients, specified as a signed or unsignednumerictypeobject. The default,numerictype(1,16)corresponds to a signed numeric type object with 16-bit coefficients and a fraction length determined based on the coefficient values, to give the best possible precision.

这个属性不是可调。

Word length of the output is same as the word length of the input. Fraction length of the output is computed such that the entire dynamic range of the output can be represented without overflow. For details on how the fraction length of the output is computed, seeFixed-Point Precision Rules for Avoiding Overflow in FIR Filters.

`RoundingMethod`—Rounding method for output fixed-point operations
`'Floor'`(default) |`'Ceiling'`|`'Convergent'`|`'Nearest'`|`'Round'`|`'Simplest'`|`'Zero'`

Rounding method for output fixed-point operations, specified as a character vector. For more information on the rounding modes, seePrecision and Range.

Usage

Syntax

y = ciccompint(x)

Description

example

y= ciccompint(x)outputs the upsampled and filtered values,y, of the input signal,x.

Input Arguments

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`x`—Data input
vector|matrix

数据输入,指定为一个向量或矩阵。的System object treats aK_i×Ninput matrix asNindependent channels, interpolating each channel over the first dimension.

This object does not support complex unsigned fixed-point data.

Output Arguments

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`y`— Upsampled and filtered signal
vector | matrix

Upsampled and filtered signal, returned as a vector or matrix. For aK_i×Ninput matrix, the result is aK_o×Noutput matrix, whereK_o=K_i×LandLis the interpolation factor.

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.CICCompensationInterpolator`

`freqz`	Frequency response of discrete-time filterSystem object
`fvtool`	Visualize frequency response of DSP filters
`info`	Information about filterSystem object
`cost`	Estimate cost of implementing filterSystem object
`coeffs`	Returns the filterSystem objectcoefficients in a structure
`polyphase`	Polyphase decomposition of multirate filter
`generatehdl`	Generate HDL code for quantized DSP filter (requiresFilter Design HDL Coder)

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

Examples

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Impulse and Frequency Response of CIC Compensation Interpolator

Open Live Script

Design an CIC compensation interpolator. Specify the interpolation factor to be 2, passband frequency to be 200 Hz, stopband frequency to be 500 Hz, and the input sample rate to be 600 Hz.

fs = 600; fPass = 200; fStop = 500; CICCompInterp = dsp.CICCompensationInterpolator(...'InterpolationFactor',2,...'PassbandFrequency',fPass,...'StopbandFrequency',fStop,...'SampleRate',fs);

Plot the impulse response. The zeroth order coefficient is delayed 6 samples, which is equal to the group delay of the filter.

fvtool(CICCompInterp,'Analysis','impulse')

Figure Figure 1: Impulse Response contains an axes object. The axes object with title Impulse Response, xlabel Time (ms), ylabel Amplitude contains an object of type stem.

Plot the magnitude and Phase response.

fvtool(CICCompInterp,'Analysis','freq')

Figure Figure 2: Magnitude Response (dB) and Phase Response contains an axes object. The axes object with title Magnitude Response (dB) and Phase Response, xlabel Frequency (Hz), ylabel Magnitude (dB) contains an object of type line.

Compensation Interpolator Design

This example uses:

Open Live Script

Design a compensation interpolator for an existing CIC interpolator having six sections and an interpolation factor of 16.

CICInterp = dsp.CICInterpolator('InterpolationFactor',16,...'NumSections',6);

Construct the compensation interpolator. Specify an interpolation factor of 2, an input sample rate of 600 Hz, a passband frequency of 100 Hz, and a stopband frequency of 250 Hz. Set the minimum attenuation of alias components in the stopband to be at least 80 dB.

fs = 600; fPass = 100; fStop = 250; ast = 80; CICCompInterp = dsp.CICCompensationInterpolator(CICInterp,...'InterpolationFactor',2,'PassbandFrequency',fPass,...'StopbandFrequency',fStop,'StopbandAttenuation',ast,...'SampleRate',fs);

Visualize the frequency response of the cascade. Normalize all magnitude responses to 0 dB.

FC = dsp.FilterCascade(CICCompInterp, CICInterp); f = fvtool(CICCompInterp,CICInterp,FC,...'Fs', [fs*2 fs*16*2 fs*16*2]); f.NormalizeMagnitudeto1 ='on'; legend(f,'CIC Compensation Interpolator','CIC Interpolator',...'Overall Response');

Figure Figure 1: Magnitude Response (dB) contains an axes object. The axes object with title Magnitude Response (dB), xlabel Frequency (kHz), ylabel Magnitude (dB) (normalized to 0 dB) contains 5 objects of type line. These objects represent CIC Compensation Interpolator, CIC Interpolator: Quantized, CIC Interpolator: Reference, Overall Response: Quantized, Overall Response: Reference.

Apply the design to a 1000-sample random input signal.

x = dsp.SignalSource(fi(rand(1000,1),1,16,15),'SamplesPerFrame',100); y = fi(zeros(32000,1),1,32,20);forind = 1:10 x2 = CICCompInterp(x()); y(((ind-1)*3200)+1:ind*3200) = CICInterp(x2);end

Algorithms

的response of a CIC filter is given by:

$H_{c i c} (ω) = {[\frac{\sin (\frac{R D ω}{2})}{\sin (\frac{ω}{2})}]}^{N}$

R,D, andNare 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:

$H_{c i c} (ω) = {[\frac{\sin (\frac{D ω}{2})}{\sin (\frac{ω}{2 R})}]}^{N}$

的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:

$H_{c i c c o m p} (ω) = {[R D \frac{\sin (\frac{ω}{2 R})}{\sin (\frac{D ω}{2})}]}^{N} for ω \leq ω_{p} < π$

whereω_pis the passband frequency of the CIC compensation filter.

Notice that whenω/2R≪ π, the previous equation forHciccomp(ω) can be simplified using the fact that sin(x) ≅x:

$H_{c i c c o m p} (ω) \approx {[\frac{(\frac{D ω}{2})}{\sin (\frac{D ω}{2})}]}^{N} = {[s i n c (\frac{D ω}{2})]}^{- N} for ω \leq ω_{p} < π$

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 MATLAB® Coder™.

Usage notes and limitations:

SeeSystem Objects in MATLAB Code Generation(MATLAB Coder).

This object supports code generation for ARM^®Cortex^®-M and ARM Cortex-A processors.

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 R2014b

dsp.CICCompensationInterpolator

Description

Creation

Syntax

Description

Properties

CICDifferentialDelay—微分延迟compens的CIC滤波器ated1(default) |positive integer scalar

CICNumSections—Number of sections of the CIC filter being compensated2(default) |positive integer scalar

CICRateChangeFactor—Rate-change factor of the CIC filter being compensated2(default) |positive integer scalar

DesignForMinimumOrder—Design filter of minimum order or of specified ordertrue(default) |false

FilterOrder—Order of interpolation compensator filter12(default) |positive integer scalar

Dependencies

InterpolationFactor—Interpolation factor of compensator2(default) |positive integer scalar

PassbandFrequency—Passband edge frequency in hertz100000(default) |positive real scalar

PassbandRipple—Filter passband ripple in decibels0.1(default) |positive real scalar

SampleRate—Input sample rate in hertz600000(default) |positive real scalar

StopbandAttenuation—Filter stopband attenuation in decibels60(default) |positive real scalar

StopbandFrequency—Stopband edge frequency in hertz400000(default) |positive real scalar

Fixed-Point Properties

CoefficientsDataType—Word and fraction lengths of coefficientsnumerictype(1,16)(default) |numerictypeobject

RoundingMethod—Rounding method for output fixed-point operations'Floor'(default) |'Ceiling'|'Convergent'|'Nearest'|'Round'|'Simplest'|'Zero'

Usage

Syntax

Description

Input Arguments

x—Data inputvector|matrix

Output Arguments

y— Upsampled and filtered signalvector | matrix

Object Functions

Specific todsp.CICCompensationInterpolator

Common to All System Objects

Examples

Impulse and Frequency Response of CIC Compensation Interpolator

Compensation Interpolator Design

Algorithms

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

Topics

`CICDifferentialDelay`—微分延迟compens的CIC滤波器ated
`1`(default) |positive integer scalar

`CICNumSections`—Number of sections of the CIC filter being compensated
`2`(default) |positive integer scalar

`CICRateChangeFactor`—Rate-change factor of the CIC filter being compensated
`2`(default) |positive integer scalar

`DesignForMinimumOrder`—Design filter of minimum order or of specified order
`true`(default) |`false`

`FilterOrder`—Order of interpolation compensator filter
12(default) |positive integer scalar

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

`PassbandFrequency`—Passband edge frequency in hertz
`100000`(default) |positive real scalar

`PassbandRipple`—Filter passband ripple in decibels
`0.1`(default) |positive real scalar

`SampleRate`—Input sample rate in hertz
`600000`(default) |positive real scalar

`StopbandAttenuation`—Filter stopband attenuation in decibels
`60`(default) |positive real scalar

`StopbandFrequency`—Stopband edge frequency in hertz
`400000`(default) |positive real scalar

`CoefficientsDataType`—Word and fraction lengths of coefficients
`numerictype(1,16)`(default) |`numerictype`object

`RoundingMethod`—Rounding method for output fixed-point operations
`'Floor'`(default) |`'Ceiling'`|`'Convergent'`|`'Nearest'`|`'Round'`|`'Simplest'`|`'Zero'`

`x`—Data input
vector|matrix

`y`— Upsampled and filtered signal
vector | matrix

Specific to`dsp.CICCompensationInterpolator`

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™.