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| kb:wss_processes_lti_systems [2021-05-05 01:04] – ↷ Page moved from kb:probstat:wss_processes_lti_systems to kb:wss_processes_lti_systems jaeyoung | kb:wss_processes_lti_systems [2024-04-30 04:03] (current) – external edit 127.0.0.1 | ||
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| - | ====== | + | ====== LTI filtering of WSS processes |
| - | Let $x(\dot)$ be a [[kb:probstat: | + | Let $x(\dot)$ be a [[kb: |
| * Mean $\mu_x$ | * Mean $\mu_x$ | ||
| Line 12: | Line 12: | ||
| $$ E[y(t)] = H(j0) \mu_x $$ | $$ E[y(t)] = H(j0) \mu_x $$ | ||
| - | $$ R_{yx}{\tau} = h \ast R_{xx}(\tau) $$ | + | $$ R_{yx}(\tau) = h \ast R_{xx}(\tau) $$ |
| $$ C_{yx}(\tau) = h \ast C_{xx} (\tau) $$ | $$ C_{yx}(\tau) = h \ast C_{xx} (\tau) $$ | ||