Figure 1 shows a system which consists of an interconnection of two discrete-time LTI systems with...

 

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Figure 1 shows a system which consists of an interconnection of two discrete-time LTI systems with impulse responses h₁ [n] and h₂[n]. x[n] | | L__ h₁ [n] = ß & [n − 1] + h[n] Figure 1 h₂ [n] = a^u[n] Į y[n] (a) Find the impulse response h[n] of the overall system. (b) Find the system transfer function (2) of the overall system, which is equal to Y(z)/X(2) where X(z) and Y(z) are the z transforms of the input x[n] and output y[n], respectively. (c) Write down the difference equation that relates x[n] and y[n]. (d) Is the system causal? (e) Under what condition would the system be stable? Figure 1 shows a system which consists of an interconnection of two discrete-time LTI systems with impulse responses h₁ [n] and h₂[n]. x[n] | | L__ h₁ [n] = ß & [n − 1] + h[n] Figure 1 h₂ [n] = a^u[n] Į y[n] (a) Find the impulse response h[n] of the overall system. (b) Find the system transfer function (2) of the overall system, which is equal to Y(z)/X(2) where X(z) and Y(z) are the z transforms of the input x[n] and output y[n], respectively. (c) Write down the difference equation that relates x[n] and y[n]. (d) Is the system causal? (e) Under what condition would the system be stable?