Back
0

Z-Transforms

Description: This quiz will test your understanding of Z-Transforms, a mathematical tool used to analyze discrete-time signals and systems.
Number of Questions: 14
Created by:
Tags: z-transforms discrete-time signals systems analysis
Start the Quiz
Attempted 0/14 Correct 0 Score 0
‹
›

What is the Z-Transform of the sequence (x[n] = a^n), where (a) is a constant?

  1. (X(z) = \frac{z}{z - a})

  2. (X(z) = \frac{z}{z + a})

  3. (X(z) = \frac{1}{z - a})

  4. (X(z) = \frac{1}{z + a})

Show answer
Correct Option: A
Explanation:

The Z-Transform of (x[n] = a^n) is (X(z) = \sum_{n=0}^\infty a^n z^{-n} = \frac{z}{z - a}).

What is the Z-Transform of the unit step sequence (u[n])?

  1. (U(z) = \frac{1}{1 - z^{-1}})

  2. (U(z) = \frac{z}{z - 1})

  3. (U(z) = \frac{1}{z - 1})

  4. (U(z) = \frac{z}{1 - z^{-1}})

Show answer
Correct Option: A
Explanation:

The Z-Transform of (u[n]) is (U(z) = \sum_{n=0}^\infty z^{-n} = \frac{1}{1 - z^{-1}}).

What is the Z-Transform of the sequence (x[n] = n)?

  1. (X(z) = \frac{z}{(z - 1)^2})

  2. (X(z) = \frac{z^2}{(z - 1)^2})

  3. (X(z) = \frac{1}{(z - 1)^2})

  4. (X(z) = \frac{z}{(z + 1)^2})

Show answer
Correct Option: A
Explanation:

The Z-Transform of (x[n] = n) is (X(z) = \sum_{n=0}^\infty n z^{-n} = \frac{z}{(z - 1)^2}).

What is the Z-Transform of the sequence (x[n] = \sin(\omega_0 n))?

  1. (X(z) = \frac{z \sin(\omega_0)}{z^2 - 2z \cos(\omega_0) + 1})

  2. (X(z) = \frac{z \cos(\omega_0)}{z^2 - 2z \sin(\omega_0) + 1})

  3. (X(z) = \frac{z}{z^2 - 2z \cos(\omega_0) + 1})

  4. (X(z) = \frac{z}{z^2 - 2z \sin(\omega_0) + 1})

Show answer
Correct Option: A
Explanation:

The Z-Transform of (x[n] = \sin(\omega_0 n)) is (X(z) = \sum_{n=0}^\infty \sin(\omega_0 n) z^{-n} = \frac{z \sin(\omega_0)}{z^2 - 2z \cos(\omega_0) + 1}).

What is the Z-Transform of the sequence (x[n] = \cos(\omega_0 n))?

  1. (X(z) = \frac{z^2 - 1}{z^2 - 2z \cos(\omega_0) + 1})

  2. (X(z) = \frac{z^2 + 1}{z^2 - 2z \cos(\omega_0) + 1})

  3. (X(z) = \frac{z}{z^2 - 2z \cos(\omega_0) + 1})

  4. (X(z) = \frac{1}{z^2 - 2z \cos(\omega_0) + 1})

Show answer
Correct Option: A
Explanation:

The Z-Transform of (x[n] = \cos(\omega_0 n)) is (X(z) = \sum_{n=0}^\infty \cos(\omega_0 n) z^{-n} = \frac{z^2 - 1}{z^2 - 2z \cos(\omega_0) + 1}).

What is the Z-Transform of the sequence (x[n] = e^{\alpha n}), where (\alpha) is a constant?

  1. (X(z) = \frac{z}{z - e^{\alpha}})

  2. (X(z) = \frac{1}{z - e^{\alpha}})

  3. (X(z) = \frac{z}{z + e^{\alpha}})

  4. (X(z) = \frac{1}{z + e^{\alpha}})

Show answer
Correct Option: A
Explanation:

The Z-Transform of (x[n] = e^{\alpha n}) is (X(z) = \sum_{n=0}^\infty e^{\alpha n} z^{-n} = \frac{z}{z - e^{\alpha}}).

What is the Z-Transform of the sequence (x[n] = \delta[n]), where (\delta[n]) is the unit impulse function?

  1. (X(z) = 1)

  2. (X(z) = z)

  3. (X(z) = \frac{1}{z})

  4. (X(z) = 0)

Show answer
Correct Option: A
Explanation:

The Z-Transform of (x[n] = \delta[n]) is (X(z) = \sum_{n=0}^\infty \delta[n] z^{-n} = 1).

What is the Z-Transform of the sequence (x[n] = n^2)?

  1. (X(z) = \frac{z}{(z - 1)^3})

  2. (X(z) = \frac{z^2}{(z - 1)^3})

  3. (X(z) = \frac{1}{(z - 1)^3})

  4. (X(z) = \frac{z}{(z + 1)^3})

Show answer
Correct Option: A
Explanation:

The Z-Transform of (x[n] = n^2) is (X(z) = \sum_{n=0}^\infty n^2 z^{-n} = \frac{z}{(z - 1)^3}).

What is the Z-Transform of the sequence (x[n] = \cos(\omega_0 n) + j \sin(\omega_0 n))?

  1. (X(z) = \frac{z(z - \cos(\omega_0))}{z^2 - 2z \cos(\omega_0) + 1})

  2. (X(z) = \frac{z(z + \cos(\omega_0))}{z^2 - 2z \cos(\omega_0) + 1})

  3. (X(z) = \frac{z}{z^2 - 2z \cos(\omega_0) + 1})

  4. (X(z) = \frac{1}{z^2 - 2z \cos(\omega_0) + 1})

Show answer
Correct Option: A
Explanation:

The Z-Transform of (x[n] = \cos(\omega_0 n) + j \sin(\omega_0 n)) is (X(z) = \sum_{n=0}^\infty (\cos(\omega_0 n) + j \sin(\omega_0 n)) z^{-n} = \frac{z(z - \cos(\omega_0))}{z^2 - 2z \cos(\omega_0) + 1}).

What is the Z-Transform of the sequence (x[n] = \left{\begin{array}{ll} 1, & n = 0\ 2, & n = 1\ 3, & n = 2\ 0, & \text{otherwise} \end{array}\right.)?

  1. (X(z) = \frac{z^2 + 2z + 3}{z^3})

  2. (X(z) = \frac{z^2 - 2z + 3}{z^3})

  3. (X(z) = \frac{z^2 + 2z - 3}{z^3})

  4. (X(z) = \frac{z^2 - 2z - 3}{z^3})

Show answer
Correct Option: A
Explanation:

The Z-Transform of (x[n]) is (X(z) = \sum_{n=0}^\infty x[n] z^{-n} = 1 + 2z^{-1} + 3z^{-2} = \frac{z^2 + 2z + 3}{z^3}).

What is the Z-Transform of the sequence (x[n] = \left{\begin{array}{ll} 1, & n \text{ is even}\ 0, & n \text{ is odd} \end{array}\right.)?

  1. (X(z) = \frac{1}{1 - z^{-2}})

  2. (X(z) = \frac{z}{1 - z^{-2}})

  3. (X(z) = \frac{1}{1 + z^{-2}})

  4. (X(z) = \frac{z}{1 + z^{-2}})

Show answer
Correct Option: A
Explanation:

The Z-Transform of (x[n]) is (X(z) = \sum_{n=0}^\infty x[n] z^{-n} = 1 + z^{-2} + z^{-4} + \cdots = \frac{1}{1 - z^{-2}}).

What is the Z-Transform of the sequence (x[n] = n \cos(\omega_0 n))?

  1. (X(z) = \frac{z(z - \cos(\omega_0))}{(z - \cos(\omega_0))^2 + \sin^2(\omega_0)})

  2. (X(z) = \frac{z(z + \cos(\omega_0))}{(z + \cos(\omega_0))^2 + \sin^2(\omega_0)})

  3. (X(z) = \frac{z}{(z - \cos(\omega_0))^2 + \sin^2(\omega_0)})

  4. (X(z) = \frac{1}{(z - \cos(\omega_0))^2 + \sin^2(\omega_0)})

Show answer
Correct Option: A
Explanation:

The Z-Transform of (x[n] = n \cos(\omega_0 n)) is (X(z) = \sum_{n=0}^\infty n \cos(\omega_0 n) z^{-n} = \frac{z(z - \cos(\omega_0))}{(z - \cos(\omega_0))^2 + \sin^2(\omega_0)}).

What is the Z-Transform of the sequence (x[n] = \left{\begin{array}{ll} 1, & n = 0\ -1, & n \text{ is odd}\ 0, & n \text{ is even and } n \ne 0 \end{array}\right.)?

  1. (X(z) = \frac{1 - z^{-1}}{1 + z^{-1}})

  2. (X(z) = \frac{1 + z^{-1}}{1 - z^{-1}})

  3. (X(z) = \frac{1}{1 + z^{-1}})

  4. (X(z) = \frac{1}{1 - z^{-1}})

Show answer
Correct Option: A
Explanation:

The Z-Transform of (x[n]) is (X(z) = \sum_{n=0}^\infty x[n] z^{-n} = 1 - z^{-1} - z^{-3} - z^{-5} + \cdots = \frac{1 - z^{-1}}{1 + z^{-1}}).

What is the Z-Transform of the sequence (x[n] = \left{\begin{array}{ll} 1, & n = 0\ 2, & n = 1\ 3, & n = 2\ 4, & n = 3\ 0, & \text{otherwise} \end{array}\right.)?

  1. (X(z) = \frac{1 + 2z^{-1} + 3z^{-2} + 4z^{-3}}{1 - z^{-1}})

  2. (X(z) = \frac{1 + 2z^{-1} + 3z^{-2} + 4z^{-3}}{1 + z^{-1}})

  3. (X(z) = \frac{1 - 2z^{-1} + 3z^{-2} - 4z^{-3}}{1 - z^{-1}})

  4. (X(z) = \frac{1 - 2z^{-1} + 3z^{-2} - 4z^{-3}}{1 + z^{-1}})

Show answer
Correct Option: A
Explanation:

The Z-Transform of (x[n]) is (X(z) = \sum_{n=0}^\infty x[n] z^{-n} = 1 + 2z^{-1} + 3z^{-2} + 4z^{-3} = \frac{1 + 2z^{-1} + 3z^{-2} + 4z^{-3}}{1 - z^{-1}}).

- Hide questions
ADVERTISEMENT

Find more quizzes from top tags

general knowledge
3615 Quizzes
119858 Questions
 technology
307 Quizzes
36705 Questions
 sports
963 Quizzes
19148 Questions
 history
1187 Quizzes
13475 Questions
 physics
598 Quizzes
13441 Questions
 biology
1160 Quizzes
12174 Questions
 science & technology
551 Quizzes
11015 Questions
 chemistry
490 Quizzes
9892 Questions
 maths
518 Quizzes
9324 Questions
 softskills
0 Quizzes
7131 Questions