The Z-transform of e^-t sampled at 10 Hz will be:

Question 9

The Z-transform of e^-t sampled at 10 Hz will be:

1. z / (z - 10)
2. z / (z - 0.1)
3. z / (z - 0.9)
4. z / (z - 1.1)

Options:

• Option 1 (ID = 12993)
• Option 2 (ID = 12994)
• Option 3 (ID = 12995)
• Option 4 (ID = 12996)

Answer: 3
Solution:

z-transform of aⁿ equals to

1/{1 - a z^(-1)} and |z| > |a|

So, z-transform of e^(-t) equals to

1/{1 - e^(-t) z^(-1)} and |e^(-t)| > |a|

Given z is sampled at 10 Hz, so t = 1/f = 1/10 = 0.1

Now, 1/{1 - e^(-t) z^(-1)} becomes

1/{1 - e^(-0.1) z^(-1)}

or, z/{z - e^(-0.1)}

or, z/{z - 0.9}   as e^(-0.1) = 0.9

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