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Question

For any random process \(X_{t}\), the Autocorrelation at time instants \(t_{1}\) and \(t_{2}\) is: [...]

Answer

\(\displaystyle\mathbf{E}[X_{t_{1}}X_{t_{2}}]=\int_{\Omega}X_{t_{1}}(\alpha)X_{t_{2}}(\alpha)P(d\alpha)=\int_{\mathbb{R}^{2}}x_{1}x_{2}\mu_{t_{1}t_{2}}(dx_{1}\times dx_{2})\)

where \(\mu_{t_{1}t_{2}}(dx_{1}\times dx_{2})\) is a joint probability distribution.

Question

For any random process \(X_{t}\), the Autocorrelation at time instants \(t_{1}\) and \(t_{2}\) is: [...]

Answer

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Question

For any random process \(X_{t}\), the Autocorrelation at time instants \(t_{1}\) and \(t_{2}\) is: [...]

Answer

\(\displaystyle\mathbf{E}[X_{t_{1}}X_{t_{2}}]=\int_{\Omega}X_{t_{1}}(\alpha)X_{t_{2}}(\alpha)P(d\alpha)=\int_{\mathbb{R}^{2}}x_{1}x_{2}\mu_{t_{1}t_{2}}(dx_{1}\times dx_{2})\)

where \(\mu_{t_{1}t_{2}}(dx_{1}\times dx_{2})\) is a joint probability distribution.

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**随机过程的自相关函数**

For any random process \(X_{t}\), the Autocorrelation at time instants \(t_{1}\) and \(t_{2}\) is: \(\displaystyle\mathbf{E}[X_{t_{1}}X_{t_{2}}]=\int_{\Omega}X_{t_{1}}(\alpha)X_{t_{2}}(\alpha)P(d\alpha)=\int_{\mathbb{R}^{2}}x_{1}x_{2}\mu_{t_{1}t_{2}}(dx_{1}\times dx_{2})\) where \(\mu_{t_{1}t_{2}}(dx_{1}\times dx_{2})\) is a joint probability distribution.

For any random process \(X_{t}\), the Autocorrelation at time instants \(t_{1}\) and \(t_{2}\) is: \(\displaystyle\mathbf{E}[X_{t_{1}}X_{t_{2}}]=\int_{\Omega}X_{t_{1}}(\alpha)X_{t_{2}}(\alpha)P(d\alpha)=\int_{\mathbb{R}^{2}}x_{1}x_{2}\mu_{t_{1}t_{2}}(dx_{1}\times dx_{2})\) where \(\mu_{t_{1}t_{2}}(dx_{1}\times dx_{2})\) is a joint probability distribution.

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
---|---|---|---|---|---|---|---|

repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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