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dsp.CICCompensationInterpolator

Compensate for CIC interpolation filter using FIR interpolator

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:

  1. Create the dsp.CICCompensationInterpolator 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?

Creation

Description

ciccompint = dsp.CICCompensationInterpolator returns 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 the InterpolationFactor property set to interp.

ciccompint = dsp.CICCompensationInterpolator(cic) returns a CIC compensation interpolator System object, ciccompint, with the CICRateChangeFactor, CICNumSections, and CICDifferentialDelay properties specified in the dsp.CICInterpolator System object cic.

ciccompint = dsp.CICCompensationInterpolator(cic,interp) returns a CIC compensation interpolator System object, ciccompint, with the CICRateChangeFactor, CICNumSections, and CICDifferentialDelay properties specified in the dsp.CICInterpolator System object cic, and the InterpolationFactor property set to interp.

ciccompint = dsp.CICCompensationInterpolator(___,Name=Value) returns a CIC compensation interpolator object with properties specified by one or more name-value pair arguments. Unspecified properties have default values.

example

Properties

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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.

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

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

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

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

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

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

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

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Since R2024a

Option to set frequencies in normalized units, specified as one of these values:

  • true –– The passband frequency Fpass and stopband frequency Fstop must be in the normalized frequency units and must be in the range Fpass < Fstop < 1.0.

    When you set the NormalizedFrequency property to true while creating the object and you do not set the passband and stopband frequencies, the object automatically sets the default values to normalized frequency units using the default sample rate of 600 kHz.

    ciccompint = dsp.CICCompensationInterpolator(NormalizedFrequency=true)
    
    ciccompint = 
      dsp.CICCompensationInterpolator with properties:
    
          CICRateChangeFactor: 2
               CICNumSections: 2
         CICDifferentialDelay: 1
          InterpolationFactor: 2
          NormalizedFrequency: true
        DesignForMinimumOrder: true
            PassbandFrequency: 0.1667
            StopbandFrequency: 0.6667
               PassbandRipple: 0.1000
          StopbandAttenuation: 60
    

    When you set the NormalizedFrequency property to true after you create the object, you must specify the passband and stopband frequencies in normalized units before you run the object algorithm.

    ciccompint = dsp.CICCompensationInterpolator
    
    ciccompint = 
      dsp.CICCompensationInterpolator with properties:
    
          CICRateChangeFactor: 2
               CICNumSections: 2
         CICDifferentialDelay: 1
          InterpolationFactor: 2
          NormalizedFrequency: false
        DesignForMinimumOrder: true
            PassbandFrequency: 100000
            StopbandFrequency: 400000
               PassbandRipple: 0.1000
          StopbandAttenuation: 60
                   SampleRate: 600000
    

    To specify the normalized frequency value, set NormalizedFrequency to true and manually convert the frequency value in Hz to the normalized value using the input sample rate in Hz. For example, if the input sample rate Fs is 600 kHz, the corresponding passband frequency value in normalized units is FpassHz/Fs and the corresponding stopband frequency in normalized units is FstopHz/Fs.

    ciccompint = dsp.CICCompensationInterpolator;
    ciccompint.NormalizedFrequency = true;
    ciccompint.PassbandFrequency = 100000/600000;
    ciccompint.StopbandFrequency = 400000/600000
    
    ciccompint = 
      dsp.CICCompensationInterpolator with properties:
    
          CICRateChangeFactor: 2
               CICNumSections: 2
         CICDifferentialDelay: 1
          InterpolationFactor: 2
          NormalizedFrequency: true
        DesignForMinimumOrder: true
            PassbandFrequency: 0.1667
            StopbandFrequency: 0.6667
               PassbandRipple: 0.1000
          StopbandAttenuation: 60
    

  • false –– The passband and stopband frequency values are in Hz. You can specify the input sample rate through the SampleRate property.

Data Types: logical

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

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

Dependencies

This property applies only when you set the DesignForMinimumOrder property to false.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Passband edge frequency Fpass, specified as a positive real scalar in Hz or in normalized frequency units (since R2024a).

If you set the NormalizedFrequency property to:

  • false –– The value of the passband frequency is in Hz and must be in the range Fpass < Fstop < Fs, where Fstop is the stopband frequency and Fs is the input sample rate.

  • true –– The value of the passband frequency is in normalized frequency units and must be in the range Fpass < Fstop < 1.0.

    When you set the NormalizedFrequency property to true while creating the object and you do not set the passband frequency, the object automatically sets the default passband frequency to normalized frequency units using the default sample rate of 600 kHz.

    ciccompint = dsp.CICCompensationInterpolator(NormalizedFrequency=true)
    
    ciccompint = 
      dsp.CICCompensationInterpolator with properties:
    
          CICRateChangeFactor: 2
               CICNumSections: 2
         CICDifferentialDelay: 1
          InterpolationFactor: 2
          NormalizedFrequency: true
        DesignForMinimumOrder: true
            PassbandFrequency: 0.1667
            StopbandFrequency: 0.6667
               PassbandRipple: 0.1000
          StopbandAttenuation: 60
    

    When you set the NormalizedFrequency property to true after you create the object, you must specify the passband frequency in normalized units before you run the object algorithm.

    ciccompint = dsp.CICCompensationInterpolator
    ciccompint = 
      dsp.CICCompensationInterpolator with properties:
    
          CICRateChangeFactor: 2
               CICNumSections: 2
         CICDifferentialDelay: 1
          InterpolationFactor: 2
          NormalizedFrequency: false
        DesignForMinimumOrder: true
            PassbandFrequency: 100000
            StopbandFrequency: 400000
               PassbandRipple: 0.1000
          StopbandAttenuation: 60
                   SampleRate: 600000
    

    To specify the normalized frequency value, set NormalizedFrequency to true and manually convert the frequency value in Hz to the normalized value using the input sample rate in Hz. For example, if the input sample rate Fs is 600 kHz, the corresponding passband frequency value in normalized units is FpassHz/Fs.

    ciccompint.NormalizedFrequency = true;
    ciccompint.PassbandFrequency = 100000/600000
    ciccompint = 
      dsp.CICCompensationInterpolator with properties:
    
          CICRateChangeFactor: 2
               CICNumSections: 2
         CICDifferentialDelay: 1
          InterpolationFactor: 2
          NormalizedFrequency: true
        DesignForMinimumOrder: true
            PassbandFrequency: 0.1667
            StopbandFrequency: 400000
               PassbandRipple: 0.1000
          StopbandAttenuation: 60
    

(since R2024a)

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Stopband edge frequency Fstop, specified as a positive real scalar in Hz or in normalized frequency units (since R2024a).

If you set the NormalizedFrequency property to:

  • false –– The value of the stopband frequency is in Hz and must be in the range Fpass < Fstop < Fs, where Fpass is the passband frequency and Fs is the input sample rate.

  • true –– The value of the stopband frequency is in normalized frequency units and must be in the range Fpass < Fstop < 1.0.

    When you set the NormalizedFrequency property to true while creating the object and you do not set the stopband frequency, the object automatically sets the default stopband frequency to normalized frequency units using the default sample rate of 600 kHz.

    ciccompint = dsp.CICCompensationInterpolator(NormalizedFrequency=true)
    
    ciccompint = 
      dsp.CICCompensationInterpolator with properties:
    
          CICRateChangeFactor: 2
               CICNumSections: 2
         CICDifferentialDelay: 1
          InterpolationFactor: 2
          NormalizedFrequency: true
        DesignForMinimumOrder: true
            PassbandFrequency: 0.1667
            StopbandFrequency: 0.6667
               PassbandRipple: 0.1000
          StopbandAttenuation: 60
    

    When you set the NormalizedFrequency property to true after you create the object, you must specify the passband frequency in normalized units before you run the object algorithm.

    ciccompint = dsp.CICCompensationInterpolator
    ciccompint = 
      dsp.CICCompensationInterpolator with properties:
    
          CICRateChangeFactor: 2
               CICNumSections: 2
         CICDifferentialDelay: 1
          InterpolationFactor: 2
          NormalizedFrequency: false
        DesignForMinimumOrder: true
            PassbandFrequency: 100000
            StopbandFrequency: 400000
               PassbandRipple: 0.1000
          StopbandAttenuation: 60
                   SampleRate: 600000
    

    To specify the normalized frequency value, set NormalizedFrequency to true and manually convert the frequency value in Hz to the normalized value using the input sample rate in Hz. For example, if the input sample rate Fs is 600 kHz, the corresponding stopband frequency value in normalized units is FstopHz/Fs.

    ciccompint.NormalizedFrequency = true;
    ciccompint.StopbandFrequency = 400000/600000
    ciccompint = 
      dsp.CICCompensationInterpolator with properties:
    
          CICRateChangeFactor: 2
               CICNumSections: 2
         CICDifferentialDelay: 1
          InterpolationFactor: 2
          NormalizedFrequency: true
        DesignForMinimumOrder: true
            PassbandFrequency: 100000
            StopbandFrequency: 0.6667
               PassbandRipple: 0.1000
          StopbandAttenuation: 60
    

(since R2024a)

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

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

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

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

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

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

Dependencies

To enable this property, set the NormalizedFrequency property to false.

Data Types: single | double

Fixed-Point Properties

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

Word and fraction lengths of coefficients, specified as a signed or unsigned numerictype object. 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.

This property is not tunable.

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, see Fixed-Point Precision Rules for Avoiding Overflow in FIR Filters.

Usage

Description

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

example

Input Arguments

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Data input, specified as a vector or a matrix. The System object treats a Ki × N input matrix as N independent channels, interpolating each channel over the first dimension.

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

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | fi
Complex Number Support: Yes

Output Arguments

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Upsampled and filtered signal, returned as a vector or matrix. For a Ki × N input matrix, the result is a Ko × N output matrix, where Ko = Ki × L and L is the interpolation factor.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | fi
Complex Number Support: Yes

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)

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freqzFrequency response of discrete-time filter System object
freqzmrCompute DTFT approximation of impulse response of multirate or single-rate filter
filterAnalyzerAnalyze filters with Filter Analyzer app
infoInformation about filter System object
costEstimate cost of implementing filter System object
coeffsReturns the filter System object coefficients in a structure
polyphasePolyphase decomposition of multirate filter
outputDelayDetermine output delay of single-rate or multirate filter
generatehdlGenerate HDL code for quantized DSP filter (requires Filter Design HDL Coder)
stepRun System object algorithm
releaseRelease resources and allow changes to System object property values and input characteristics
resetReset internal states of System object

Examples

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Create a dsp.CICCompensationDecimator object with default settings. While creating the object, set the NormalizedFrequency property to true so that the passband and the stopband frequencies are in normalized frequency units.

CICCompInterp = dsp.CICCompensationInterpolator(...
    NormalizedFrequency=true)
CICCompInterp = 
  dsp.CICCompensationInterpolator with properties:

      CICRateChangeFactor: 2
           CICNumSections: 2
     CICDifferentialDelay: 1
      InterpolationFactor: 2
      NormalizedFrequency: true
    DesignForMinimumOrder: true
        PassbandFrequency: 0.1667
        StopbandFrequency: 0.6667
           PassbandRipple: 0.1000
      StopbandAttenuation: 60

  Use get to show all properties

Plot the impulse response of the filter. The zeroth order coefficient is delayed by 7 samples, which is equal to the group delay of the filter.

impz(CICCompInterp)

Figure contains an axes object. The axes object with title Impulse Response, xlabel n (samples), ylabel Amplitude contains an object of type stem.

Plot the magnitude and phase responses of the filter.

freqz(CICCompInterp)

Figure contains 2 axes objects. Axes object 1 with title Phase, xlabel Normalized Frequency (\times\pi rad/sample), ylabel Phase (degrees) contains an object of type line. Axes object 2 with title Magnitude, xlabel Normalized Frequency (\times\pi rad/sample), ylabel Magnitude (dB) contains an object of type line.

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)
CICInterp = 
  dsp.CICInterpolator with properties:

    InterpolationFactor: 16
      DifferentialDelay: 1
            NumSections: 6
     FixedPointDataType: 'Full precision'

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)
CICCompInterp = 
  dsp.CICCompensationInterpolator with properties:

      CICRateChangeFactor: 16
           CICNumSections: 6
     CICDifferentialDelay: 1
      InterpolationFactor: 2
    DesignForMinimumOrder: true
        PassbandFrequency: 100
        StopbandFrequency: 250
           PassbandRipple: 0.1000
      StopbandAttenuation: 80
               SampleRate: 600

  Show all properties

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);
for ind = 1:10
    x2 = CICCompInterp(x());
    y(((ind-1)*3200)+1:ind*3200) = CICInterp(x2);
end

Algorithms

The response of a CIC filter is given by:

Hcic(ω)=[sin(RDω2)sin(ω2)]N

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

After decimation, the CIC response has the form:

Hcic(ω)=[sin(Dω2)sin(ω2R)]N

The normalized version of this last response is the one that the CIC compensator needs to compensate. Hence, the passband response of the CIC compensator should take the following form:

Hciccomp(ω)=[RDsin(ω2R)sin(Dω2)]Nforωωp<π

where ωp is the passband frequency of the CIC compensation filter.

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

Hciccomp(ω)[(Dω2)sin(Dω2)]N = [sinc(Dω2)]Nforωωp<π

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

Extended Capabilities

Version History

Introduced in R2014b

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