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.

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 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.

`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.

`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 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.

`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. PassbandFrequency must be less than F_s/2, where F_s is 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. StopbandFrequency must be less than F_s/2, where F_s is 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 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.

`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.

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

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
`fvtool`	Visualize frequency response of DSP filters
`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
`generatehdl`	Generate HDL code for quantized DSP filter (requires Filter Design HDL Coder)

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

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')

Plot the magnitude and Phase response.

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

Compensation Interpolator Design

This example uses:

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) becomes step(obj,x).

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');

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 of the CIC filter, respectively.

After decimation, the cic response has the form:okay

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

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.

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

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

Documentation

dsp.CICCompensationInterpolator

Description

Creation

Syntax

Description

Properties

CICDifferentialDelay — Differential delay of the CIC filter being compensated 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

Dependencies

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

Fixed-Point Properties

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'

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™.

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

See Also

Functions

Objects

Topics

DSP System Toolbox Documentation

Support

`CICDifferentialDelay` — Differential delay of the CIC filter being compensated
`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™.

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