# polyphase

Polyphase decomposition of multirate filter

## Syntax

``p = polyphase(sysobj)``
``p = polyphase(sysobj,Arithmetic=arithType)``

## Description

example

````p = polyphase(sysobj)` returns the polyphase matrix `p` of the multirate filter System object™ `sysobj`. Each row in the matrix corresponds to a polyphase branch. The number of columns in `p` corresponds to the number of filter taps per polyphase branch.```
````p = polyphase(sysobj,Arithmetic=arithType)` returns the polyphase matrix `p` in the precision set by the `arithType`.```

## Examples

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When you create a multirate filter that uses polyphase decomposition, the `polyphase` function lets you analyze the component filters individually by returning the components as rows in a matrix. First, create an interpolate-by-three filter.

`hs = dsp.FIRInterpolator`
```hs = dsp.FIRInterpolator with properties: InterpolationFactor: 3 NumeratorSource: 'Property' Numerator: [0 -1.2906e-04 -2.2804e-04 0 5.5461e-04 8.0261e-04 0 -0.0015 -0.0020 0 0.0034 0.0043 0 -0.0067 -0.0083 0 0.0121 0.0145 0 -0.0205 -0.0241 0 0.0332 0.0388 0 -0.0530 -0.0620 0 0.0861 0.1027 0 -0.1540 -0.1976 0 ... ] (1x72 double) Use get to show all properties ```

In this syntax, the matrix `p` contains all of the subfilters, one filter per matrix row.

`p = polyphase(hs)`
```p = 3×24 0 0 0 0 0 0 0 0 0 0 0 0 1.0000 0 0 0 0 0 0 0 0 0 0 0 -0.0001 0.0006 -0.0015 0.0034 -0.0067 0.0121 -0.0205 0.0332 -0.0530 0.0861 -0.1540 0.4088 0.8247 -0.1976 0.1027 -0.0620 0.0388 -0.0241 0.0145 -0.0083 0.0043 -0.0020 0.0008 -0.0002 -0.0002 0.0008 -0.0020 0.0043 -0.0083 0.0145 -0.0241 0.0388 -0.0620 0.1027 -0.1976 0.8247 0.4088 -0.1540 0.0861 -0.0530 0.0332 -0.0205 0.0121 -0.0067 0.0034 -0.0015 0.0006 -0.0001 ```

Finally, to analyze the component filters individually, use one of the analysis functions on the corresponding polyphase component vector. For example, to plot the impulse response of the first component filter, use `impz` on the first vector of the polyphase matrix.

`impz(p(1,:))`

## Input Arguments

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Input filter, specified as one of the following filter System objects:

Specify the arithmetic used in computing the polyphase matrix. When you specify `'double'` or `'single'`, the function performs double- or single-precision analysis. When you specify `'fixed'` , the arithmetic changes depending on the setting of the `CoefficientDataType` property and whether the System object is locked or unlocked.

Details for Fixed-Point Arithmetic

System Object StateCoefficient Data TypeRule
Unlocked`'Same as input'`The function assumes that the coefficient data type is signed, 16 bit, and autoscaled. The function performs fixed-point analysis based on this assumption.
Unlocked`'Custom'`The function performs fixed-point analysis based on the setting of the `CustomCoefficientsDataType` property.
Locked`'Same as input'`When the input data type is `'double'` or `'fixed'`, the function assumes that the coefficient data type is signed, 16-bit, and autoscaled. The function performs fixed-point analysis based on this assumption.
Locked`'Custom'`The function performs fixed-point analysis based on the setting of the `CustomCoefficientsDataType` property.

When you do not specify the arithmetic for non-CIC structures, the function uses double-precision arithmetic if the filter System object is in an unlocked state. If the System object is locked, the function performs analysis based on the locked input data type. CIC structures only support fixed-point arithmetic.

## Output Arguments

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Polyphase matrix `p` of the multirate filter. Each row in the matrix corresponds to a polyphase branch. The first row of matrix `p` represents the first polyphase branch, the second row the second polyphase branch, and so on to the last polyphase branch. The number of columns in `p` corresponds to the number of filter taps per polyphase branch.

## Version History

Introduced in R2011a

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