Consider a causal LTI system with impulse response h[n], and input x[n] = x 1 [n] x 1 [n 2] + x 1 [n 4]

Consider a causal LTI system with impulse response h[n], and input x[n] = x₁[n] ˆ’ x₁[n ˆ’ 2] + x₁[n ˆ’ 4] where x₁[n] = u[n]ˆ’ u[n ˆ’ 2]. The impulse response of the system is h[n] = u[n] ˆ’ u[n ˆ’ 2]

(a) Use the convolution sum to find the output of the system, y[n].

(b) If the given system is cascaded with another causal LTI system with impulse response g[n], we know the overall impulse response of the two cascaded systems is

Find the impulse response g[n].

n = 0, 3 hT[n] = %3D otherwise