# 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:

1. Create the dsp.CICInterpolator object and set its properties.

2. Call the object with arguments, as if it were a function.

## Creation

### 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.

Factor by which the input signal is interpolated, specified as a positive integer.

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

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.

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

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.

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

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.

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'.

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

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'.

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

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'.

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

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'.

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

## Usage

### Description

example

cicInterpOut = cicInterp(input) interpolates the input using a CIC interpolator.

### Input Arguments

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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.

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

### Output Arguments

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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:

$\begin{array}{l}W{L}_{\text{output}}=W{L}_{\text{input}}+NumSect\\ F{L}_{\text{output}}=F{L}_{\text{input}}\end{array}$

where,

• WLoutput –– Word length of the output data.

• FLoutput –– Fraction length of the output data.

• WLinput –– Word length of the input data.

• FLinput –– Fraction length of the input data.

• NumSect –– Number of sections in the CIC filter specified through the NumSections property.

WLinput and FLinput 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, FLoutput is given by the following equation:

$F{L}_{\text{output}}=W{L}_{\text{output}}-\left(W{L}_{\text{input}}-F{L}_{\text{input}}+NumSect\right)$

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, FLoutput is given by the following equation:

$F{L}_{\text{output}}=W{L}_{\text{output}}-\left(W{L}_{\text{input}}-F{L}_{\text{input}}+NumSect\right)$

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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 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 discrete-time filter System object phasez Phase response of discrete-time filter System object (unwrapped) fvtool Visualize frequency response of DSP filters gain Gain of CIC filter System object getFixedPointInfo Get fixed-point word and fraction lengths info Information about filter System object
 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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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 a fixed-point signal by a factor of 2 from 22.05 kHz to 44.1 kHz.

cicint = dsp.CICInterpolator(2)
cicint =
dsp.CICInterpolator with properties:

InterpolationFactor: 2
DifferentialDelay: 1
NumSections: 2
FixedPointDataType: 'Full precision'

Create a dsp.SineWave object with SampleRate set to 22.05 kHz, SamplesPerFrame set to 32, and OutputDataType set to 'Custom'. To generate a fixed-point signal, set the CustomOutputDataType property to a numerictype object. For the purpose of this example, set the value to numerictype([],16). The fraction length is computed based on the values of the generated sinusoidal signal to give the best possible precision.

To generate a fixed-point signal, set the Method property of the dsp.SineWave object to 'Table lookup'. This method of generating the sinusoidal signal requires that the period of every sinusoid in the output be evenly divisible by the sample period. That is, $1/{\mathit{f}}_{\mathit{i}}{\mathit{T}}_{\mathit{s}}={\mathit{k}}_{\mathit{i}}$ must be an integer value for every channel i = 1, 2, ..., N. The value of ${\mathit{T}}_{\mathit{s}}$ equals $1/{\mathit{F}}_{\mathit{s}}$, the variable ${\mathit{f}}_{\mathit{i}}$ is the frequency of the sinusoidal signal, and ${\mathit{F}}_{\mathit{s}}$ is the sample rate of the signal. In other words, the ratio ${\mathit{F}}_{\mathit{s}}/{\mathit{f}}_{\mathit{i}}$ must be an integer. For more details, see the Algorithms section on the dsp.SineWave object page.

In this example, ${\mathit{F}}_{\mathit{s}}$ is set to 22050 Hz and ${\mathit{f}}_{\mathit{i}}$ is set to 1050 Hz.

Fs = 22.05e3;
sine = dsp.SineWave('Frequency',1050,'SampleRate',Fs,'SamplesPerFrame',32,...
'Method','Table lookup','OutputDataType','Custom')
sine =
dsp.SineWave with properties:

Amplitude: 1
Frequency: 1050
PhaseOffset: 0
ComplexOutput: false
Method: 'Table lookup'
TableOptimization: 'Speed'
SampleRate: 22050
SamplesPerFrame: 32
OutputDataType: 'Custom'

Show all properties

In each loop of the iteration, stream in a frame of the fixed-point sinusoidal signal sampled at 22.05 kHz. Interpolate the streamed signal by a factor of 2. The interpolated output has 64 samples per frame.

for i = 1:16
x = sine();
y = cicint(x);
end

The output of the CIC interpolation filter is amplified by a specific gain value. You can determine this value using the gain function. This gain equals the gain of the $2{\mathit{N}}^{\mathrm{th}}$ stage of the CIC interpolation filter and equals ${\left(\mathit{I}×\mathit{D}\right)}^{\mathit{N}}/\mathit{I}$, where $\mathit{I}$ is the interpolation factor, $\mathit{D}$ is the differential delay, and $\mathit{N}$ is the number of sections of the CIC interpolator.

gainCIC = gain(cicint)
gainCIC = 2

To adjust this amplified output and to match it to the amplitude of the original signal, divide the CIC interpolated signal with the computed gain value.

Compare the last frames of the original and the interpolated signals. While plotting, account for the output latency of 2 samples.

n = (0:63)';
stem(n(1:31)/Fs, double(x(1:31)),'r','filled')
hold on;
I = cicint.InterpolationFactor;
stem(n(1:61)/(Fs*I), ...
double(y(4:end))/gainCIC,'b')
xlabel('Time (sec)')
ylabel('Signal Amplitude')
legend('Original Signal','Interpolated Signal',...
'location','north')
hold off;

Using the info function in the '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 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 : 14  14  14  14
Output  word length      : 17
Output  fraction length  : 14
'

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.

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## 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

### Topics

Introduced in R2012a

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