Predicting Extraction for an Existing Tower with a Given Number of Steps. An existing tower contains 5.0 theoretical steps. It is desired to predict its performance under the following conditions….
Write the integral expression for the two-parameter output correlation function over the time intervals .
Consider the following mean-square differential equation,
driven by a WSS random process with psd
The differential equation is subject to the initial condition , where the random variable has zero-mean, variance 5, and is orthogonal to the input random process .
(a) As a preliminary step, express the deterministic solution to the above differential equation, now regarded as an ordinary differential equation with deterministic input and initial condition , 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 as a mean-square convolution integral of the input process over the time interval plus a zero-input term due to the random initial condition . Justify the mean-square existence of the terms in your solution.
(c) Write the integral expression for the two-parameter output correlation function over the time intervals . You do not have to evaluate the integral.