Show pageOld revisionsBacklinksExport to PDFBack to top This page is read only. You can view the source, but not change it. Ask your administrator if you think this is wrong. ====== Random processes ====== ===== Properties of random processes ===== * Expected value of signal at time $t$: $$ \mu_X(t) = E[X(t)] $$ * Autocorrelation of signal at times $t_1$ and $t_2$: $$ R_{XX}(t_1, t_2) = E[X(t_1)X(t_2)] $$ * Autocovariance of signal at times $t_1$ and $t_2$: $$ C_{XX}(t_1, t_2) = E[\tilde{X}(t_1)\tilde{X}(t_2)] = R_{XX}(t_1, t_2) - \mu_X(t_1)\mu_X(t_2) $$ where $\tilde{X}(t) = X(t) - \mu_X(t)$ ===== Properties of two random processes ===== * Cross-correlation of $X(t_1)$ and $Y(t_2): $$ R_{XY}(t_1, t_2) = E[X(t_1)Y(t_2)] $$ * Cross-covariance of $X(t_1)$ and $Y(t_2): $$ C_{XY}(t_1, t_2) = E[\tilde{X}(t_1)\tilde{Y}(t_2)] $$ kb/random_processes.txt Last modified: 2024-04-30 04:03by 127.0.0.1