(a) Write, as a series, the z-transform of the number sequence generated by sampling the time function e(t) = ε^−t every T seconds, beginning at t = 0 . Can you express this transform in closed form?

(b) Evaluate the coefficients in the series of part

(a) for the case that T = 0.05 s .

(c) The exponential e(t) = ε^−bt is sampled every T = 0.2 s , yielding the z-transform

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E(z) 1 8 () = + ( ) + ( ) +1/2 = -2 Evaluate b.