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 3.7 Continuous-Time Models of Discrete-Time Systems The function ToContinuousTime, when applied to discrete-time objects, converts them to the continuous-time domain. In many respects ToContinuousTime behaves as an inverse function to ToDiscreteTime and applies inverse algorithms to those described previously in Section 3.5. Again, the methods can be chosen through the Method option, which accepts the same values. The conversion attempts to find the slowest possible continuous-time model the outputs of which would match the ones of the discrete-time model at the sample time. Finding continuous-time equivalents of discrete-time systems. Here a continuous-time system from an earlier example is converted to the discrete-time domain. In[71]:= Out[71]= This brings the system back to continuous time. In[72]:= Out[72]= As our sampling period T is real-valued, we can simplify the result and see that the system is the same as the one we started with. In[73]:= Out[73]= Here is the lag system used earlier. In[74]:= Out[74]= This converts the system to the discrete-time domain using the bilinear transformation with frequency prewarping. In[75]:= Out[75]= This brings the system back to continuous time. In[76]:= Out[76]= This is the discrete-time approximation of the lag system obtained with the first-order hold. In[77]:= Out[77]= This converts the result back to continuous time. In[78]:= Out[78]= Note that in the case of the FirstOrderHold method, ToContinuousTime cannot use the inverse of the state-space algorithm implemented in ToDiscreteTime and, as an exception, resorts to the conversion using transfer functions, which is less efficient.