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:

Create the dsp.CICCompensationInterpolator object and set its properties.
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

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.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.

`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.

`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.

`CICDifferentialDelay` — Differential delay of the CIC filter being compensated
`1` (default) | positive integer scalar

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

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

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

`NormalizedFrequency` — Option to set frequencies in normalized units
`false` (default) | `true`

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 Fpass_Hz/Fs and the corresponding stopband frequency in normalized units is Fstop_Hz/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

`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 is true, 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 the DesignForMinimumOrder property to false.

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

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

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)

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

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 Fstop_Hz/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)

`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.

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

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

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

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

`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, see Precision and Range.

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

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

Syntax

y = ciccompint(x)

Description

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

example

Input Arguments

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`x` — Data input
vector | matrix

Data input, specified as a vector or a matrix. The System object treats a K_i × N input matrix as N independent 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 a K_i × N input matrix, the result is a K_o × N output matrix, where K_o = K_i × L and L is 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 named obj, use this syntax:

release(obj)

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Specific to `dsp.CICCompensationInterpolator`

`freqz`	Frequency response of discrete-time filter System object
`freqzmr`	Compute DTFT approximation of impulse response of multirate or single-rate filter
`filterAnalyzer`	Analyze filters with Filter Analyzer app
`info`	Information about filter System object
`cost`	Estimate cost of implementing filter System object
`coeffs`	Returns the filter System object coefficients in a structure
`polyphase`	Polyphase decomposition of multirate filter
`outputDelay`	Determine output delay of single-rate or multirate filter
`generatehdl`	Generate HDL code for quantized DSP filter (requires Filter Design HDL Coder) (To be removed)

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

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Impulse and Frequency Response of CIC Compensation Interpolator

Open Live Script

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)

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

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)

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:

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

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:

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

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:

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

where ω_p 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:

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

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:

See System 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 VHDL, Verilog and SystemVerilog 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, see Generate HDL Code for Filter System Objects (Filter Design HDL Coder).

Version History

Introduced in R2014b

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R2024a: Support for normalized frequencies

When you set the NormalizedFrequency property to true, you must specify the passband frequency and stopband frequency in normalized frequency units (0 to 1). For more information, see the NormalizedFrequency property description.

dsp.CICCompensationInterpolator

Description

Creation

Syntax

Description

Properties

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

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

CICDifferentialDelay — Differential delay of the CIC filter being compensated 1 (default) | positive integer scalar

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

NormalizedFrequency — Option to set frequencies in normalized units false (default) | true

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

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

Dependencies

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

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

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

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

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

Dependencies

Fixed-Point Properties

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

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

Usage

Syntax

Description

Input Arguments

x — Data input vector | matrix

Output Arguments

y — Upsampled and filtered signal vector | matrix

Object Functions

Specific to dsp.CICCompensationInterpolator

Common to All System Objects

Examples

Impulse and Frequency Response of CIC Compensation Interpolator

Compensation Interpolator Design

Algorithms

Extended Capabilities

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

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

Version History

R2024a: Support for normalized frequencies

See Also

Functions

Objects

Topics

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

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

`CICDifferentialDelay` — Differential delay of the CIC filter being compensated
`1` (default) | positive integer scalar

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

`NormalizedFrequency` — Option to set frequencies in normalized units
`false` (default) | `true`

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

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

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

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

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

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

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

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

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

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