The inverse Z-transform of 𝑧/(𝑧−𝑎) (for |𝑧|𝑎) is 𝑎^n. So, the correct answer is c) 𝑎^n. Here's a step-by-step explanation: 1. The Z-transform pairs are defined as 𝑧^n ↔ 𝑎^n, where ↔ denotes a transform pair. 2. The given function is 𝑧/(𝑧−𝑎), which can be rewritten as 1/(1-𝑎/𝑧) by dividing the numerator and denominator by 𝑧. 3. This is now in the form of a geometric series, which has the sum 1/(1-x) = ∑x^n for |x|

Question

The inverse Z-transform of 𝑧/(𝑧−𝑎) (for |𝑧|>𝑎) is 𝑎^n. So, the correct answer is c) 𝑎^n.

Here's a step-by-step explanation:

1. The Z-transform pairs are defined as 𝑧^n ↔ 𝑎^n, where ↔ denotes a transform pair.

2. The given function is 𝑧/(𝑧−𝑎), which can be rewritten as 1/(1-𝑎/𝑧) by dividing the numerator and denominator by 𝑧.

3. This is now in the form of a geometric series, which has the sum 1/(1-x) = ∑x^n for |x|<1.

4. Comparing this with the standard Z-transform pairs, we can see that the inverse Z-transform is 𝑎^n.

So, the correct answer is c) 𝑎^n.

Knowee AI · Accepted Answer

The inverse Z-transform of 𝑧/(𝑧−𝑎) (for |𝑧|>𝑎) is 𝑎^n. So, the correct answer is c) 𝑎^n.

Here's a step-by-step explanation:

1. The Z-transform pairs are defined as 𝑧^n ↔ 𝑎^n, where ↔ denotes a transform pair.

2. The given function is 𝑧/(𝑧−𝑎), which can be rewritten as 1/(1-𝑎/𝑧) by dividing the numerator and denominator by 𝑧.

3. This is now in the form of a geometric series, which has the sum 1/(1-x) = ∑x^n for |x|<1.

4. Comparing this with the standard Z-transform pairs, we can see that the inverse Z-transform is 𝑎^n.

So, the correct answer is c) 𝑎^n.

Which of the following is the inverse Z - transform of 𝑧𝑧−𝑎(∣𝑧∣>𝑎)z−az (∣z∣>a) ?a)𝑎−𝑛a −n b)ac)𝑎𝑛a n d)1𝑎a1