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.

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.VariableBandwidthFIRFilter

• dsp.VariableBandwidthIIRFilter

arithType — Arithmetic type

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

Specify the arithmetic used during analysis. When the arithmetic input is not specified and the filter System object is unlocked, the analysis tool assumes a double-precision filter. The 'Arithmetic' property set to 'Fixed' applies only to filter System objects with fixed-point properties.

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