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# Documentation

## Supported Models for Time- and Frequency-Domain Data

### Supported Models for Time-Domain Data

#### Continuous-Time Models

You can directly estimate the following types of continuous-time models:

You can also use d2c to convert an estimated discrete-time model into a continuous-time model.

#### Discrete-Time Models

You can estimate all linear and nonlinear models supported by the System Identification Toolbox™ product as discrete-time models, except process models, which are defined only in continuous-time..

#### ODEs (Grey-Box Models)

You can estimate both continuous-time and discrete-time models from time-domain data for linear and nonlinear differential and difference equations.

#### Nonlinear Models

You can estimate discrete-time Hammerstein-Wiener and nonlinear ARX models from time-domain data.

You can also estimate nonlinear grey-box models from time-domain data. See Estimating Nonlinear Grey-Box Models.

### Supported Models for Frequency-Domain Data

There are two types of frequency-domain data:

• Frequency response data

• Frequency domain input/output signals which are Fourier Transforms of the corresponding time domain signals.

The data is considered continuous-time if its sample time (Ts) is 0, and is considered discrete-time if the sample time is nonzero.

#### Continuous-Time Models

You can estimate the following types of continuous-time models directly:

You can also use d2c to convert an estimated discrete-time model into a continuous-time model.

#### Discrete-Time Models

You can estimate all linear model types supported by the System Identification Toolbox product as discrete-time models, except process models, which are defined in continuous-time only. For estimation of discrete-time models, you must use discrete-time data.

The noise component of a model cannot be estimated using frequency domain data, with the exception of ARX models. Thus, the K matrix of an identified state-space model, the noise component, is zero. An identified polynomial model has output-error (OE) or ARX structure; BJ/ARMAX or other polynomial structure with nontrivial values of C or D polynomials cannot be estimated.

#### ODEs (Grey-Box Models)

For linear grey-box models, you can estimate both continuous-time and discrete-time models from frequency-domain data. The noise component of the model, the K matrix, cannot be estimated using frequency domain data; it remains fixed to 0.

Nonlinear grey-box models are supported only for time-domain data.

#### Nonlinear Black-Box Models

Nonlinear black box (nonlinear ARX and Hammerstein-Wiener models) cannot be estimated using frequency domain data.