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Consider the following mean-square differential equation,

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driven by a WSS random process Best Essay Writing Services | EssayBureau.com with psd

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The differential equation is subject to the initial condition Best Essay Writing Services | EssayBureau.com, where the random variable Best Essay Writing Services | EssayBureau.com has zero-mean, variance 5, and is orthogonal to the input random process Best Essay Writing Services | EssayBureau.com.

(a) As a preliminary step, express the deterministic solution to the above differential equation, now regarded as an ordinary differential equation with deterministic input Best Essay Writing Services | EssayBureau.comand initial condition Best Essay Writing Services | EssayBureau.com, not a random variable. Write your solution as the sum of a zero-input part and a zero-state part.

(b) Now returning to the m.s. differential equation, write the solution random process Best Essay Writing Services | EssayBureau.com as a mean-square convolution integral of the input process Best Essay Writing Services | EssayBureau.com over the time interval Best Essay Writing Services | EssayBureau.com plus a zero-input term due to the random initial condition Best Essay Writing Services | EssayBureau.com. Justify the mean-square existence of the terms in your solution.

(c) Write the integral expression for the two-parameter output correlation function Best Essay Writing Services | EssayBureau.com over the time intervals Best Essay Writing Services | EssayBureau.com. You do not have to evaluate the integral.

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