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tf

Convert discrete-time filter System object to transfer function

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Syntax

[num,den] = tf(sysobj)
[num,den] = tf(sysobj,Arithmetic=arithType)

Description

[num,den] = tf(sysobj) converts the discrete-time filter System object™ to numerator and denominator coefficient vectors of the equivalent transfer function.

example

[num,den] = tf(sysobj,Arithmetic=arithType) analyzes the filter System object based on the arithmetic specified in arithType.

For more input options, see tf in Signal Processing Toolbox™.

Examples

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Open Live Script

Compute the transfer function of an SOS filter using the tf function.

Create a fourth-order, lowpass SOS filter object with a normalized cutoff frequency of 0.4.

[z,p,k] = ellip(4,1,60,0.4);    % Set up the filter
[sosMatrix,scaleValues] = zp2sos(z,p,k);
[num,den] = sos2ctf(sosMatrix);
sosFilt = dsp.SOSFilter(Structure='Direct form I',...
    Numerator=num,Denominator=den,...
    ScaleValues=scaleValues)
sosFilt = 
  dsp.SOSFilter with properties:

            Structure: 'Direct form I'
    CoefficientSource: 'Property'
            Numerator: [2x3 double]
          Denominator: [2x3 double]
       HasScaleValues: true
          ScaleValues: [0.0351 1 1]

  Use get to show all properties

Compute the transfer function of the designed SOS filter. The tf function returns the numerator and the denominator coefficient vectors of the filter.

[numTF,denTF] = tf(sosFilt)
numTF = 1×5

    0.0351    0.1038    0.1432    0.1038    0.0351


denTF = 1×5

    1.0000   -1.5676    1.7412   -1.0104    0.3093

Input Arguments

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Arithmetic used in the filter analysis, specified as 'double', 'single', or 'Fixed'. When the arithmetic input is not specified and the filter System object is unlocked, the analysis tool assumes a double-precision filter. When the arithmetic input is not specified and the System object is locked, the function performs the analysis based on the data type of the locked input.

The 'Fixed' value applies to filter System objects with fixed-point properties only.

When the 'Arithmetic' input argument is specified as 'Fixed' and the filter object has the data type of the coefficients set to 'Same word length as input', the arithmetic analysis depends on whether the System object is unlocked or locked.

  • unlocked –– The analysis object function cannot determine the coefficients data type. The function assumes that the coefficients data type is signed, has a 16-bit word length, and is auto scaled. The function performs fixed-point analysis based on this assumption.

  • locked –– When the input data type is 'double' or 'single', the analysis object function cannot determine the coefficients data type. The function assumes that the data type of the coefficients is signed, has a 16-bit word length, and is auto scaled. The function performs fixed-point analysis based on this assumption.

To check if the System object is locked or unlocked, use the isLocked function.

When the arithmetic input is specified as 'Fixed' and the filter object has the data type of the coefficients set to a custom numeric type, the object function performs fixed-point analysis based on the custom numeric data type.

Output Arguments

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Numerator coefficients of the filter, returned as a row vector.

Data Types: double

Denominator coefficients of the filter, returned as a row vector.

Data Types: double

Version History

Introduced in R2011a

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See Also

Functions

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