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  2. Discrete time and continuous time - Wikipedia

    en.wikipedia.org/wiki/Discrete_time_and...

    Unlike a continuous-time signal, a discrete-time signal is not a function of a continuous argument; however, it may have been obtained by sampling from a continuous-time signal. When a discrete-time signal is obtained by sampling a sequence at uniformly spaced times, it has an associated sampling rate. Discrete-time signals may have several ...

  3. Discrete system - Wikipedia

    en.wikipedia.org/wiki/Discrete_system

    A computer is a finite-state machine that may be viewed as a discrete system. Because computers are often used to model not only other discrete systems but continuous systems as well, methods have been developed to represent real-world continuous systems as discrete systems. One such method involves sampling a continuous signal at discrete time ...

  4. Continuous simulation - Wikipedia

    en.wikipedia.org/wiki/Continuous_simulation

    Discrete event simulation, on the other hand, changes state variables only in response to events, typically using next-event time progression. Continuous dynamic systems can only be captured by a continuous simulation model, while discrete dynamic systems can be captured either in a more abstract manner by a continuous simulation model (like ...

  5. Bilinear transform - Wikipedia

    en.wikipedia.org/wiki/Bilinear_transform

    The bilinear transform is a first-order Padé approximant of the natural logarithm function that is an exact mapping of the z-plane to the s-plane.When the Laplace transform is performed on a discrete-time signal (with each element of the discrete-time sequence attached to a correspondingly delayed unit impulse), the result is precisely the Z transform of the discrete-time sequence with the ...

  6. Discretization - Wikipedia

    en.wikipedia.org/wiki/Discretization

    In applied mathematics, discretization is the process of transferring continuous functions, models, variables, and equations into discrete counterparts. This process is usually carried out as a first step toward making them suitable for numerical evaluation and implementation on digital computers.

  7. Transfer function - Wikipedia

    en.wikipedia.org/wiki/Transfer_function

    Instead of using the Laplace transform (which is better for continuous-time signals), discrete-time signals are dealt with using the z-transform (notated with a corresponding capital letter, like () and ()), so a discrete-time system's transfer function can be written as:

  8. Dynamical systems theory - Wikipedia

    en.wikipedia.org/wiki/Dynamical_systems_theory

    When difference equations are employed, the theory is called discrete dynamical systems. When the time variable runs over a set that is discrete over some intervals and continuous over other intervals or is any arbitrary time-set such as a Cantor set, one gets dynamic equations on time scales.

  9. Lyapunov equation - Wikipedia

    en.wikipedia.org/wiki/Lyapunov_equation

    In particular, the discrete-time Lyapunov equation (also known as Stein equation) for is A X A H − X + Q = 0 {\displaystyle AXA^{H}-X+Q=0} where Q {\displaystyle Q} is a Hermitian matrix and A H {\displaystyle A^{H}} is the conjugate transpose of A {\displaystyle A} , while the continuous-time Lyapunov equation is