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The output y[n] of a discrete time LTI system is related to the input x(n) as given below:
∞ y(n) = ∑ x(k) k = 0
Which one of the following correctly relates the z-transform of the input and output, denoted by x(z) and y(z), respectively?
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- Y(z) = (1 – z– 1) X(z)
- Y(z) = z– 1 X(z)
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Y(z) = X(z) 1 – z– 1 -
Y(z) = dX (z) dz
Correct Option: C
Given,
| ∞ | ||
| y(n) = | ∑ | x(k) |
| k = 0 |
which represents an accumulator, whose z-transform is
| Y(z) = | · X(z) | z – 1 |
| or Y(z) = | 1 – z– 1 |
Hence, alternative (C) is the correct choice.
