Ergodic process - Wikipedia
In physics, statistics, econometrics and signal processing, a stochastic process is said to be in an ergodic regime if an observable's ensemble average equals the time average. [1] In this regime, any collection of random samples from a process must represent the average statistical properties of the entire regime.
random process, such as mean, autocorrelation, n-th-order distribution • We define two types of stationarity: strict sense (SSS) and wide sense (WSS) • A random process X(t) (or X n ) is said to be SSS if all its finite order
So a sinusoid at random phase is an ergodic process. Indeed, this form is a foundation for modeling natural random processes such as ocean waves, atmospheric conditions, and various types of noise. In particular, it can be verified that the construction N y(t) = an cos(ωnt + θn), n=1
A random process is called a strongly stationary process or Strict Sense Stationary Process (SSS Process) if all its finite dimensional distribution are invariance under translation of time 't'.
Ergodicity - Wikipedia
In mathematics, ergodicity expresses the idea that a point of a moving system, either a dynamical system or a stochastic process, will eventually visit all parts of the space that the system moves in, in a uniform and random sense. This implies that the average behavior of the system can be deduced from the trajectory of a "typical" point.
Ergodic Processes - ECE Department
Ergodic processes are processes for which time and ensemble (statistical) averages are interchangeable. The concept of ergodicity deals with the equality of time and statistical averages. Definition: Time Average : If X (t) is a random process, then is called the time-average of X (t) over (-T, T) and is denoted by. Note:
Stationary ergodic process - Wikipedia
In probability theory, a stationary ergodic process is a stochastic process which exhibits both stationarity and ergodicity. In essence this implies that the random process will not change its statistical properties with time and that its statistical properties (such as the theoretical mean and variance of the process) can be deduced from a ...
A random process is ergodic if time-averages are the same for all sample functions, and are equal to the corresponding ensamble averages. In an ergodic process, all its statistics can be obtained from a single sample function.
2005年2月24日 · Given a random process that is stationary and ergodic, with an expected value of zero and autocorrelation R () t , the power spectral density, or spectrum, of the random process is defined as the Fourier transform of the autocorrelation.
A random process X(t) is applied as input to a linear time-invariant filter of impulse response h(t), • It produces a random process Y (t) at the filter output as
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