dsp.CICInterpolator

Interpolate signal using cascaded integrator-comb filter

Description

The dsp.CICInterpolator System object™ interpolates an input signal using a cascaded integrator-comb (CIC) interpolation filter. The CIC interpolation filter structure consists of N sections of cascaded comb filters, followed by a rate change by a factor of R, followed by N sections of cascaded integrators. For details, see Algorithms. The NumSections property specifies N, the number of sections in the CIC filter. The InterpolationFactor property specifies R, the interpolation factor. The getFixedPointInfo function returns the word lengths and fraction lengths of the fixed-point sections and the output for the dsp.CICInterpolator System object. You can also generate HDL code for this System object using the generatehdl function.

Note

This object requires a Fixed-Point Designer™ license.

To interpolate a signal using a CIC filter:

Create the dsp.CICInterpolator 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? (MATLAB).

Creation

Syntax

cicInterp = dsp.CICInterpolator

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

cicInterp = dsp.CICInterpolator(Name,Value)

Description

example

cicInterp = dsp.CICInterpolator creates 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 the InterpolationFactor property set to R, the DifferentialDelay property set to M, and the NumSections property set to N.

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 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 (MATLAB).

`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

Differential delay value used in each of the comb sections of the filter, specified as a positive integer. For details, see Algorithms. If the differential delay is of built-in integer class data type, the interpolation factor must be the same integer data type or double. For example, if the differential delay is an int8, then the interpolation factor must be an int8 or double.

`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 the OutputWordLength property. The object determines the filter section data type and the output fraction length that give the best possible precision. For details, see getFixedPointInfo and cicInterpOut argument.
Specify word lengths – Specify the word lengths of the CIC filter sections and the object output through the SectionWordLengths and OutputWordLength properties. The object determines the corresponding fraction lengths to give the best possible precision. For details, see getFixedPointInfo and the cicInterpOut argument.
Specify word and fraction lengths – Specify the word length and fraction length of the CIC filter sections and the object output through the SectionWordLengths, SectionFractionLengths, OutputWordLength, and OutputFractionLength properties.

`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]

Dependencies

This property applies when you set the FixedPointDataType property 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]

Dependencies

This property applies when you set the FixedPointDataType property 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.

Dependencies

This property applies when you set the FixedPointDataType property 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.

Dependencies

This property applies when you set the FixedPointDataType property 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

Data input, specified as a vector or matrix. If 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 is single or double, the output data type matches the input data type.

If 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 the FixedPointDataType property.

Full precision

When the FixedPointDataType property is set to 'Full precision', the 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 the NumSections property.

WL_input and FL_input are 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 the FixedPointDataType property is set to 'Minimum section word lengths', the output word length is the value you specify in OutputWordLength property. The output fraction length, FL_output is 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 the FixedPointDataType is set to 'Specify word and fraction lengths', the output word length and fraction length are the values you specify in the OutputWordLength and OutputFractionLength properties.

Specify word lengths

When the FixedPointDataType is set to 'Specify word lengths', the output word length is the value you specify in the OutputWordLength property. The output fraction length, FL_output is 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 named obj, use this syntax:

release(obj)

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Specific to dsp.CICInterpolator

`generatehdl`	Generate HDL code for quantized DSP filter (requires Filter Design HDL Coder)
`impz`	Impulse response of discrete-time filter System object
`freqz`	Frequency response of filter
`phasez`	Unwrapped phase response for filter
`fvtool`	Visualize frequency response of DSP filters
`gain`	CIC filter gain
`getFixedPointInfo`	Get fixed-point word and fraction lengths
`info`	Information about filter System object

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

For a list of filter analysis methods this object supports, type dsp.CICInterpolator.helpFilterAnalysis in the MATLAB^® command prompt. For the corresponding function reference pages, see Analysis Methods for Filter System Objects.

Examples

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Interpolate a Signal Using CICInterpolator Object

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).

Create a dsp.CICInterpolator System object™ with InterpolationFactor set to 2. Interpolate signal by a factor of 2 from 22.05 kHz to 44.1 kHz.

cicint = dsp.CICInterpolator(2);

Create fixed-point sinusoidal input signal of 512 samples, with a sampling frequency 22.05 kHz.

Fs = 22.05e3;      
n = (0:511)';      % 0.0113 sec signal
x = fi(sin(2*pi*1e3/Fs*n),true,16,15);

Create dsp.SignalSource System object.

src = dsp.SignalSource(x,32);

Interpolate the output with 64 samples per frame.

y = zeros(16,64);
for ii = 1:16
     y(ii,:) = cicint(src());   
end

Plot the first frame of the original and interpolated signals. Output latency is 2 samples.

gainCIC = ...
   (cicint.InterpolationFactor*cicint.DifferentialDelay)...
   ^cicint.NumSections/cicint.InterpolationFactor;
stem(n(1:31)/Fs, double(x(1:31)),'r','filled')
hold on; 
stem(n(1:61)/(Fs*cicint.InterpolationFactor), ...
   double(y(1,4:end))/gainCIC,'b') 
xlabel('Time (sec)')
ylabel('Signal Amplitude')
legend('Original signal','Interpolated signal',...
   'location','north')
hold off;

Using the info method in '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 : 15  15  15  15
     Output  word length      : 17
     Output  fraction length  : 15
     '

Determine the Section and Output Word Lengths and Fraction Lengths

Open Live Script

Using the getFixedPointInfo function, you can determine the word lengths and fraction lengths of the fixed-point sections and the output of the dsp.CICDecimator and dsp.CICInterpolator System objects. The data types of the filter sections and the output depend on the FixedPointDataType property of the filter System object™.

Full precision

Create a dsp.CICDecimator object. The default value of the NumSections property is 2. This value indicates that there are two integrator and comb sections. The WLs and FLs vectors returned by the getFixedPointInfo function 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, the FixedPointDataType property of the object is set to 'Full precision'. Calling the getFixedPointInfo function 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 = 1×5

    18    18    18    18    18

FLs = 1×5

    15    15    15    15    15

For details on how the word lengths and fraction lengths are computed, see the description for Output Arguments.

If you lock the cicD object by passing an input to its algorithm, you do not need to pass the nt argument to the getFixedPointInfo function.

input = int64(randn(8,1))

input = 8x1 int64 column vector

    1
    2
   -2
    1
    0
   -1
    0
    0

output = cicD(input)

output=4×1 object
     0
     1
     3
     0

          DataTypeMode: Fixed-point: binary point scaling
            Signedness: Signed
            WordLength: 66
        FractionLength: 0

[WLs,FLs] = getFixedPointInfo(cicD) %#ok

WLs = 1×5

    66    66    66    66    66

FLs = 1×5

     0     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 the FixedPointDataType property 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 object
    3.5784   -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 = 1×5

    26    26    26    26    32

FLs = 1×5

    15    15    15    15    21

Specify word and fraction lengths

Change the FixedPointDataType property to 'Specify word and fraction lengths'. Determine the fixed-point information using the getFixedPointInfo function.

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 = 1×5

    16    16    16    16    32

FLs = 1×5

     0     0     0     0     0

The section and output word lengths and fraction lengths are assigned as per the respective fixed-point properties of the cicD object. These values are not determined by the input numeric type. To confirm, call the getFixedPointInfo function without passing the numerictype input argument.

[WLs, FLs] = getFixedPointInfo(cicD) %#ok

WLs = 1×5

    16    16    16    16    32

FLs = 1×5

     0     0     0     0     0

Specify word lengths

To specify the word lengths of the filter section and output, set the FixedPointDataType property 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

The getFixedPointInfo function 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 = 1×5

    16    16    16    16    32

FLs = 1×5

     5     5     5     5    21

For more details on how the function computes the word and fraction lengths, see the description for Output 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 filter H(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_C is the transfer function of the comb part of the filter.
H_I is the transfer function of the integrator part of the filter.
N is the number of sections. The number of sections in a CIC filter is defined as the number of sections in either the comb part or the integrator part of the filter. This value does not represent the total number of sections throughout the entire filter.
R is the interpolation factor.
M is 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 the N sections 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, see Algorithms.

Algorithms

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CIC Interpolation Filter

The filter H(z) in More About is realized as an interpolation filter when N sections of cascaded comb filters are followed by a rate change by a factor R, followed by N sections 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:

See System 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 the dsp.CICInterpolator object uses for fixed-point signals.

where,

secNT = numerictype(1,secWL,secFL)
outNT = numertictype(1,outWL,outFL)
secWL is the section word length you specify through the SectionWordLengths property.
secFL is the section fraction length you specify through the SectionFractionLengths property.
outWL is the output word length you specify through the OutputWordLength property.
outFL is the output fraction length you specify through the OutputFractionLength property.

The value of NumSections in this diagram is 2.

Documentation

dsp.CICInterpolator

Description

Note

Creation

Syntax

Description

Properties

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

Dependencies

SectionFractionLengths — Fixed-point fraction lengths for each filter section 0 (default) | scalar | vector

Dependencies

OutputWordLength — Fixed-point word length for filter output 32 (default) | scalar integer

Dependencies

OutputFractionLength — Fixed-point fraction length for filter output 0 (default) | scalar integer

Dependencies

Usage

Syntax

Description

Input Arguments

input — Data input vector | matrix

Output Arguments

cicInterpOut — CIC interpolator output vector | matrix

Object Functions

Specific to dsp.CICInterpolator

Common to All System Objects

Examples

Interpolate a Signal Using CICInterpolator 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 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

Blocks

Topics

Introduced in R2012a

DSP System Toolbox Documentation

Support

`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™.