1. The impulse response of a causal system is:h(t) = A cos(wt) e¯¹/¹u(t)where u(t) is the Heaviside step function. The response is measured experimentally with asampling interval of T.a. Write an expression for the sampled impulse response h[n].b. Calculate the z transform of h[n] and write an expression for H[z]. Use the tablesprovided below as necessary.c.Does the system have an infinite impulse response (IIR) or finite impulse response(FIR)? Justify your answer.d.What is the DC gain of H[z]?e. Write a difference equation that describes the output y[n] in terms of input x[n].

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