MathProblemsBank

15.1.24 Theory of random processes

Problem: The action of a stationary linear system is given as follows: \( \xi^{\prime \prime}+2 \xi^{\prime}+2 \xi=\eta^{\prime}+\eta \). The correlation function of the output is known: \( K_{\eta, \eta}(\tau)=\exp (-|\tau|), \tau \in(-\infty ;+\infty) \). Find the correlation function of the input.