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Transfer Function Models

Transfer function models

Transfer function models describe the relationship between the inputs and outputs of a system using a ratio of polynomials. The model order is equal to the order of the denominator polynomial. The roots of the denominator polynomial are referred to as the model poles. The roots of the numerator polynomial are referred to as the model zeros.

The parameters of a transfer function model are its poles, zeros, and transport delays.

In continuous time, a transfer function model has the following form:


Here, Y(s), U(s), and E(s) represent the Laplace transforms of the output, input, and noise, respectively. num(s) and den(s) represent the numerator and denominator polynomials that define the relationship between the input and the output.

For more information, see What are Transfer Function Models?


System IdentificationIdentify models of dynamic systems from measured data


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idtfTransfer function model with identifiable parameters
tfestEstimate transfer function model
pemPrediction error minimization for refining linear and nonlinear models
spectrumestEstimate transfer function model for power spectrum data (Since R2022b)
delayestEstimate time delay (dead time) from data
initSet or randomize initial parameter values
tfdataAccess transfer function data
getpvecObtain model parameters and associated uncertainty data
setpvecModify values of model parameters
getparObtain attributes such as values and bounds of linear model parameters
setparSet attributes such as values and bounds of linear model parameters
addMinPhaseAdd minimum phase to frequency response magnitude (Since R2022b)
tfestOptionsOption set for tfest
spectrumestOptionsOption set for spectrumest (Since R2022b)


Transfer Function Model Basics

Estimate Transfer Function Models

Frequency Domain Troubleshooting

Model Initialization and Structure Parameters