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based on an earlier version of the Wolfram Language.
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ToContinuousTimeModel

ToContinuousTimeModel[sys]
gives the continuous-time approximation of the discrete-time TransferFunctionModel or StateSpaceModel object sys.
ToContinuousTimeModel
gives the continuous-time approximation of the discrete-time TransferFunctionModel object tf, using s as the Laplace-transform variable.
  • Possible settings for the Method option include:
"ForwardRectangularRule"Euler forward method
"BackwardRectangularRule"Euler backward method
"BilinearTransform"Tustin bilinear approximation
"ZeroPoleMapping"exact matching of zeros and poles
"ZeroOrderHold"piecewise constant approximation
"FirstOrderHold"piecewise linear (triangular) approximation
  • The default setting Method->Automatic implements the bilinear transformation.
  • A bilinear transform with critical frequency radians per time unit can be specified by setting Method.
  • The method gives the non-causal first-order hold equivalent.
  • The setting Method->{m, "StateSpaceConversion"->True} computes the approximation using the state-space representation and converts the result to the transfer-function representation.
  • The setting False computes using the transfer-function object.
  • The setting Automatic computes the approximation using the transfer-function representation, except for the method.
A continuous-time approximation of a discrete-time system:
A continuous-time approximation of a discrete-time system:
In[1]:=
Click for copyable input
Out[1]=
Convert a discrete-time transfer-function model to a continuous-time model:
Convert a discrete-time state-space model to a continuous-time model:
Convert a multiple-input, multiple-output system to a continuous-time system:
Convert a symbolic system:
By default, the approximation is based on the bilinear transformation:
Specify the approximation method:
Compare various approximation methods:
An approximation that preserves the transmission at a specified frequency:
Various continuous-time approximations to a fourth-order Chebyshev II bandstop filter:
Bode plots:
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