Question

A sequence x (n) with the z-transform X (z) = Z^4 + Z^2 – 2z + 2 – 3Z^-4 is applied to an input to a linear time invariant system with the impulse response h (n) = 2δ (n-3). The output at n = 4 will be:

(a) -6

(b) Zero

(c) 2

(d) -4

I have been asked this question in unit test.

Origin of the question is The Z-Transform in section Digital Control Systems of Control Systems

Answer 1

Correct choice is (b) Zero

The best I can explain: H (z) = 2z^-3

Then taking the inverse Laplace transform of the equation of Y (z) at n=4 y(n) =0.