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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 ...
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
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.
A discrete dynamical system, discrete-time dynamical system is a tuple (T, M, Φ), where M is a manifold locally diffeomorphic to a Banach space, and Φ is a function. When T is taken to be the integers, it is a cascade or a map. If T is restricted to the non-negative integers we call the system a semi-cascade. [14]
Still in the discrete state case, letting = and assuming that the system initially is found in state , the Kolmogorov forward equations describe an initial-value problem for finding the probabilities of the process, given the quantities ().
The equations are a set of differential equations – over time – of the probabilities that the system occupies each of the different states. The name was proposed in 1940: [ 1 ] [ 2 ] When the probabilities of the elementary processes are known, one can write down a continuity equation for W, from which all other equations can be derived and ...
Related: 300 Trivia Questions and Answers to Jumpstart Your Fun Game Night What Is Today's Strands Hint for the Theme: "Moonlighting"? Today's Strands game revolves around different stages/shapes ...
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 the Lotka-Volterra equations for modeling a predator-prey eco-system) or in a more realistic manner by a discrete event simulation model (in a ...