Power contained in a random process $X(t)$

1. How do you find the power of a random process?
2. How do you calculate power from power spectral density?
3. How do you find the autocorrelation of a random process?
4. What are the statistical properties of random process?

How do you find the power of a random process?

Definition 55.1 (Expected Power) The expected power of a random process X(t) is defined as E[X(t)2]. E [ X ( t ) 2 ] . Notice that the expected power is related to the autocorrelation function (54.1) by E[X(t)2]=RX(t,t).

How do you calculate power from power spectral density?

A signal consisting of many similar subcarriers will have a constant power spectral density (PSD) over its bandwidth and the total signal power can then be found as P = PSD · BW.

How do you find the autocorrelation of a random process?

2: The autocorrelation function of a WSS random process is an even function; that is, R_XX(τ) = R_XX(−τ). This property can easily be established from the definition of autocorrelation. Note that R_xx(−τ) = E[X(t)X(t−τ)]. Since X(t) is WSS, this expression is the same for any value of t.

What are the statistical properties of random process?

Properties of Random Process

A random process is described by some properties such as the mean, autocorrelation, cross-correlation, autocovariance, power spectral density, and average power.