This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# ToContinuousTimeModel

 ToContinuousTimeModel[sys] gives the continuous-time approximation of the discrete-time TransferFunctionModel or StateSpaceModel object sys. ToContinuousTimeModelgives 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 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:
 Out[1]=
 Scope   (4)
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:
 Options   (4)
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:
 Applications   (1)
Various continuous-time approximations to a fourth-order Chebyshev II bandstop filter:
Bode plots:
ToDiscreteTimeModel is essentially the inverse of ToContinuousTimeModel:
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