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

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.

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:

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

Syntax

``cicInterpOut = cicInterp(input)``

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 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 : 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 = 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 = 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

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