Autocorrelation of the output of the LTI system.

Discussion in 'Homework Help' started by cdummie, Sep 26, 2017.

  1. cdummie

    Thread Starter Member

    Feb 6, 2015
    Let's say that we have a wide sense stationary process x(t) with autocorrelation $$R_{XX}(ζ)=Ae^{-a|ζ|}$$ (where both a and ζ are positive) at the input of Linear Time Invariant system whose impulse response is $$h(t)=e^{-bt}u(t), b>0$$ where $$u(t)$$ is a Heaviside function. Find autocorrelation function at the output of the LTI system.

    When i have a "regular" signal at the input of the LTI system i can find the output as a correlation of the input signal and impulse response of the LTI system, now i don't have expression for the input signal in time domain i only have it's autocorrelation function, how am i supposed to determine autocorrelation of the output?