ToDiscreteTimeModel
ToDiscreteTimeModel [lsys,τ]
gives the discrete-time approximation, with sampling period τ, of the continuous-time systems models lsys.
ToDiscreteTimeModel [tfm,τ,z]
specifies the transform variable z.
Details and Options
- ToDiscreteTimeModel is also known as sampling.
- The systems model lsys can be a TransferFunctionModel or a StateSpaceModel .
- For a TransferFunctionModel object sys, ToDiscreteTimeModel [sys,τ] uses z as the Z-transform variable.
- ToDiscreteTimeModel accepts a Method option that can be used to specify the approximation method.
- The settings for Method are the same as for ToContinuousTimeModel .
- The setting Method->{m,"StateSpaceConversion"->Automatic } computes the approximation using the transfer-function representation, except for the "ZeroOrderHold" and "FirstOrderHold" methods.
Examples
open allclose allBasic Examples (1)
A discrete-time approximation of a continuous-time system:
Scope (6)
Convert a continuous-time transfer-function model to the discrete-time domain:
Convert a continuous-time state-space model to discrete time:
Convert a multiple-input, multiple-output system to discrete time:
Convert a symbolic system:
Convert a time-delay TransferFunctionModel :
Convert a singular descriptor StateSpaceModel :
Options (5)
Method (5)
By default, the approximation is based on the bilinear transformation:
Specify the desired approximation method:
Compare the various approximation methods:
An approximation that preserves the transmission at the specified frequency:
The bilinear and backward Euler methods may add states to descriptor state-space models:
Applications (1)
Various approximations to a fourth-order Butterworth lowpass filter:
Bode plots:
Properties & Relations (5)
A stable transfer-function model:
The "ForwardRectangularRule" method may not give a stable approximation:
The stability of the "BilinearTransform" approximation depends on the critical frequency:
Critical frequencies less than the Nyquist frequency give stable approximations:
When the critical frequency is more than the Nyquist frequency, the approximation is unstable:
All other approximations give a stable system if the continuous-time system is stable:
ToContinuousTimeModel is essentially the inverse of ToDiscreteTimeModel :
Time delays in the resulting system are given relative to the sampling period:
ToDiscreteTimeModel may add states to systems with neutral time delays:
History
Text
Wolfram Research (2010), ToDiscreteTimeModel, Wolfram Language function, https://reference.wolfram.com/language/ref/ToDiscreteTimeModel.html.
CMS
Wolfram Language. 2010. "ToDiscreteTimeModel." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ToDiscreteTimeModel.html.
APA
Wolfram Language. (2010). ToDiscreteTimeModel. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ToDiscreteTimeModel.html
BibTeX
@misc{reference.wolfram_2025_todiscretetimemodel, author="Wolfram Research", title="{ToDiscreteTimeModel}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/ToDiscreteTimeModel.html}", note=[Accessed: 12-April-2025 ]}
BibLaTeX
@online{reference.wolfram_2025_todiscretetimemodel, organization={Wolfram Research}, title={ToDiscreteTimeModel}, year={2010}, url={https://reference.wolfram.com/language/ref/ToDiscreteTimeModel.html}, note=[Accessed: 12-April-2025 ]}