# 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:

`$Y\left(s\right)=\frac{num\left(s\right)}{den\left(s\right)}U\left(s\right)+E\left(s\right)$`

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?

## Apps

 System Identification Identify models of dynamic systems from measured data

## Functions

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 `idtf` Transfer function model with identifiable parameters `tfest` Estimate transfer function model `pem` Prediction error minimization for refining linear and nonlinear models `spectrumest` Estimate transfer function model for power spectrum data
 `delayest` Estimate time delay (dead time) from data `init` Set or randomize initial parameter values
 `tfdata` Access transfer function data `getpvec` Obtain model parameters and associated uncertainty data `setpvec` Modify values of model parameters `getpar` Obtain attributes such as values and bounds of linear model parameters `setpar` Set attributes such as values and bounds of linear model parameters `addMinPhase` Add minimum phase to frequency response magnitude
 `tfestOptions` Option set for `tfest` `spectrumestOptions` Option set for `spectrumest`