Let x[n] be a real stationary white-noise sequence, with zero mean and variance 2 x .

Question:

Let x[n] be a real stationary white-noise sequence, with zero mean and variance σ²_x. Let x [n] be the input to the cascade of two causal linear time-invariant discrete-time systems, as shown in Figure

hi[n} x [n] = o? £k-0 ha[n] y[n] w [n] |(a) Is o h{[k]? (b) Is o=D oΣkE0 h[시? uk:

(c) Let h₁[n] = aⁿu[n] and h₂[n] = bⁿu[n]. Determine the impulse response of the overall system in Figure, and, from this, determine σ²_w. Are your answers to parts (b) and (c) consistent?