True or False if the same WSS random process Un is input to

True or False: if the same WSS random process U[n] is input to two different LTI systems with the following impulse responses h_1[n] = 3 delta [n] + 2 delta [n - 1] h_2[n] = 5 delta [n], the mean of the output will be the same for both systems. True False

Solution

True.....

For an LTI system whose impulse response is h(t), the output y(t) is given by the convolution + y(t) = + h(v)x(t v)dv = x(v)h(t v)dv for any specifc input x(t) for which the convolution is well-defined. The convolution is well-defined if, for instance, the input x(t) is bounded and the system is boundedinput bounded-output (BIBO) stable, i.e. h(t) is absolutely integrable

the mean of the output process is constant, and equals the mean of the input scaled by the the DC gain of the system.

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