# Wolfram Language & System 11.0 (2016)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# TransferFunctionModel

represents the model of the transfer-function matrix m with complex variable s.

TransferFunctionModel[{num,den},s]
specifies the numerator num and denominator den of a transfer-function model.

TransferFunctionModel[{z,p,g},s]
specifies the zeros z, poles p, and gain g of a transfer-function model.

gives the transfer-function model of the systems model sys.

## Details and OptionsDetails and Options

• TransferFunctionModel can represent scalar and multivariate systems in continuous or discrete time.
• Time delays can be included in any transfer-function model, by using SystemsModelDelay.
• In TransferFunctionModel[{num,den},s], num must be a matrix, and den can be specified as a matrix or just the common denominator.
• TransferFunctionModel does not cancel any pole or zero of the matrix elements.
• In , the following systems can be converted:
•  AffineStateSpaceModel approximate Taylor conversion NonlinearStateSpaceModel approximate Taylor conversion StateSpaceModel exact conversion
• The following options can be given:
•  Method Automatic the method to obtain the transfer function of a state-space model SamplingPeriod Automatic the sampling period of the system SystemsModelLabels Automatic labels for the input and output variables
• Settings for the Method option include "DeterminantExpansion", "ResolventIdentities", "Inverse", and "Generic". With a setting , the transfer-function model is computed using determinant expansion.

## ExamplesExamplesopen allclose all

### Basic Examples  (4)Basic Examples  (4)

A single-input, single-output system:

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A system with two inputs and one output:

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Obtain the transfer-function representation of a state-space model:

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A discrete-time transfer function with a sampling period of 1:

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Evaluate a transfer function over a range of frequencies:

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Plot the magnitudes:

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