polyphase

Polyphase decomposition of multirate filter

Syntax

p = polyphase(sysobj)

p = polyphase(sysobj,Arithmetic=arithType)

Description

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

Polyphase Matrix of an FIR Interpolator

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

sysobj — Input filter

filter System object

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

• dsp.CICCompensationDecimator

• dsp.CICCompensationInterpolator

• dsp.FIRDecimator

• dsp.FIRHalfbandDecimator

• dsp.FIRHalfbandInterpolator

• dsp.FIRInterpolator

• dsp.FIRRateConverter

• dsp.IIRHalfbandDecimator

• dsp.IIRHalfbandInterpolator

• dsp.VariableFIRDecimator

• dsp.VariableFIRInterpolator

arithType — Arithmetic type

'double' (default) | 'single' | 'Fixed'

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 State	Coefficient Data Type	Rule
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

p — polyphase matrix

matrix

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

R2024b: Support for dsp.VariableFIRDecimator and dsp.VariableFIRInterpolator Objects

Starting in R2024b, the polyphase analysis function supports the dsp.VariableFIRDecimator and dsp.VariableFIRInterpolator objects.

R2024a: polyphase function with no output arguments returns polyphase matrix

When you call the polyphase function with no output arguments, the function returns the polyphase matrix of the multirate filter. In previous releases, the polyphase function with no output arguments launched Filter Visualization Tool with all the polyphase subfilters to allow you to analyze each component subfilter individually.

You do not need to make any changes to your code. However, to analyze the individual subfilters, use one of the functions in the Filter Analysis category on the individual polyphase component vectors.

For example, here is the code to plot the impulse response of the first polyphase component subfilter of the default dsp.FIRInterpolator filter without using the Filter Visualization Tool.

firI = dsp.FIRInterpolator

firI = 
  dsp.FIRInterpolator with properties:

    InterpolationFactor: 3
        NumeratorSource: 'Property'
              Numerator: [0 -1.2906e-04 -2.2804e-04 0 5.5461e-04 … ] (1×72 double)

polyComp = polyphase(firI)
impz(polyComp(1,:))