tf

Convert discrete-time filter System object to transfer function

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.

[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

Transfer Function of Biquad Filter

Compute the transfer function of a biquad filter using the tf function.

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

[z,p,k] = ellip(4,1,60,0.4);    % Set up the filter
[s,g] = zp2sos(z,p,k);
biquad = dsp.BiquadFilter(s,g,'Structure','Direct form I')

biquad = 
  dsp.BiquadFilter with properties:

                       Structure: 'Direct form I'
                 SOSMatrixSource: 'Property'
                       SOSMatrix: [2x6 double]
                     ScaleValues: 0.0351
      NumeratorInitialConditions: 0
    DenominatorInitialConditions: 0
        OptimizeUnityScaleValues: true

  Show all properties

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

[num,den] = tf(biquad)

num = 1×5

    0.0351    0.1038    0.1432    0.1038    0.0351

den = 1×5

    1.0000   -1.5676    1.7412   -1.0104    0.3093

Input Arguments

sysobj — Input filter

filter System object

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

• dsp.AllpassFilter

• dsp.AllpoleFilter

• dsp.BiquadFilter

• dsp.CICCompensationDecimator

• dsp.CICCompensationInterpolator

• dsp.CICDecimator

• dsp.CICInterpolator

• dsp.CoupledAllpassFilter

• dsp.Differentiator

• dsp.FarrowRateConverter

• dsp.FilterCascade

• dsp.FIRDecimator

• dsp.FIRFilter

• dsp.FIRHalfbandDecimator

• dsp.FIRHalfbandInterpolator

• dsp.FIRInterpolator

• dsp.FIRRateConverter

• dsp.FourthOrderSectionFilter

• dsp.HighpassFilter

• dsp.IIRFilter

• dsp.IIRHalfbandDecimator

• dsp.IIRHalfbandInterpolator

• dsp.LowpassFilter

• dsp.NotchPeakFilter

• dsp.SOSFilter

• dsp.VariableBandwidthFIRFilter

• dsp.VariableBandwidthIIRFilter

arithType — Arithmetic type

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

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

num — Numerator coefficients

row vector

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

Data Types: double

den — Denominator coefficients

scalar | row vector

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

Data Types: double