Q8. Consider a linear discrete-time system S with input x and output y. Suppose S is driven by an input x(k) for 0 <= k < L to produce a zero-state output y(k). Use deconvolution to find the impulse response h(k) for 0 <= k < L if x(k) and y(k) are as follows.

x = [2, 0,1, 4]^T

y = [6, 1,4, 3] ^T

1. Get impulse response h(k) for k = 0, 1, and 2.
2. Get the same result using long division.