Electronics and Communication Engineering (ECE) Exam  >  Electronics and Communication Engineering (ECE) Questions  >  A discrete-time system is given by the equati... Start Learning for Free
A discrete-time system is given by the equation 
y(k + 3) = -0.3y(k + 2) + y(k + 1) - 0.5y(k) + 2x(k + 3) - 4x(k + 1)
The highest degree of ‘z’ in Numerator and Denominator polynomials of its transfer function H(z) will be, (Assume all initial conditions are zero).
  • a)
    2 and 3 respectively
  • b)
    3 and 3 respectively
  • c)
    3 and 2 respectively
  • d)
    3 and 4 respectively
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A discrete-time system is given by the equationy(k + 3) = -0.3y(k + 2)...
Understanding the System Equation
The given discrete-time system is represented by the equation:
y(k + 3) = -0.3y(k + 2) + y(k + 1) - 0.5y(k) + 2x(k + 3) - 4x(k + 1)
To analyze the system, we need to determine its transfer function H(z).
Transfer Function Derivation
1. Shifting Terms: The equation shows a relationship between the output y and input x at different time steps. The highest index on y is k + 3, indicating that the output depends on future inputs and past outputs.
2. Characteristic Equation: To find the transfer function H(z), we need to express the system in terms of z-transform:
- Input terms: x(k + 3) and x(k + 1) correspond to the z-transform terms z^3 and z, respectively.
- Output terms: y(k + 3), y(k + 2), y(k + 1), and y(k) correspond to z^3, z^2, z, and 1, respectively.
Determining Degrees of Polynomials
- Numerator Degree:
- The highest power of z in the input terms is from x(k + 3), which has a degree of 3.
- Denominator Degree:
- The highest power of z in the output terms is from y(k + 3), which also has a degree of 3.
Conclusion
Thus, the transfer function H(z) can be characterized as:
- Numerator Degree: 3
- Denominator Degree: 3
Therefore, the correct answer is option B: 3 and 3 respectively.
Attention Electronics and Communication Engineering (ECE) Students!
To make sure you are not studying endlessly, EduRev has designed Electronics and Communication Engineering (ECE) study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Electronics and Communication Engineering (ECE).
Explore Courses for Electronics and Communication Engineering (ECE) exam

Top Courses for Electronics and Communication Engineering (ECE)

A discrete-time system is given by the equationy(k + 3) = -0.3y(k + 2) + y(k + 1) - 0.5y(k) + 2x(k + 3) - 4x(k + 1)The highest degree of z in Numerator and Denominator polynomials of its transfer function H(z) will be, (Assume all initial conditions are zero).a)2 and 3 respectivelyb)3 and 3 respectivelyc)3 and 2 respectivelyd)3 and 4 respectivelyCorrect answer is option 'B'. Can you explain this answer?
Question Description
A discrete-time system is given by the equationy(k + 3) = -0.3y(k + 2) + y(k + 1) - 0.5y(k) + 2x(k + 3) - 4x(k + 1)The highest degree of z in Numerator and Denominator polynomials of its transfer function H(z) will be, (Assume all initial conditions are zero).a)2 and 3 respectivelyb)3 and 3 respectivelyc)3 and 2 respectivelyd)3 and 4 respectivelyCorrect answer is option 'B'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about A discrete-time system is given by the equationy(k + 3) = -0.3y(k + 2) + y(k + 1) - 0.5y(k) + 2x(k + 3) - 4x(k + 1)The highest degree of z in Numerator and Denominator polynomials of its transfer function H(z) will be, (Assume all initial conditions are zero).a)2 and 3 respectivelyb)3 and 3 respectivelyc)3 and 2 respectivelyd)3 and 4 respectivelyCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A discrete-time system is given by the equationy(k + 3) = -0.3y(k + 2) + y(k + 1) - 0.5y(k) + 2x(k + 3) - 4x(k + 1)The highest degree of z in Numerator and Denominator polynomials of its transfer function H(z) will be, (Assume all initial conditions are zero).a)2 and 3 respectivelyb)3 and 3 respectivelyc)3 and 2 respectivelyd)3 and 4 respectivelyCorrect answer is option 'B'. Can you explain this answer?.
Solutions for A discrete-time system is given by the equationy(k + 3) = -0.3y(k + 2) + y(k + 1) - 0.5y(k) + 2x(k + 3) - 4x(k + 1)The highest degree of z in Numerator and Denominator polynomials of its transfer function H(z) will be, (Assume all initial conditions are zero).a)2 and 3 respectivelyb)3 and 3 respectivelyc)3 and 2 respectivelyd)3 and 4 respectivelyCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Electronics and Communication Engineering (ECE). Download more important topics, notes, lectures and mock test series for Electronics and Communication Engineering (ECE) Exam by signing up for free.
Here you can find the meaning of A discrete-time system is given by the equationy(k + 3) = -0.3y(k + 2) + y(k + 1) - 0.5y(k) + 2x(k + 3) - 4x(k + 1)The highest degree of z in Numerator and Denominator polynomials of its transfer function H(z) will be, (Assume all initial conditions are zero).a)2 and 3 respectivelyb)3 and 3 respectivelyc)3 and 2 respectivelyd)3 and 4 respectivelyCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of A discrete-time system is given by the equationy(k + 3) = -0.3y(k + 2) + y(k + 1) - 0.5y(k) + 2x(k + 3) - 4x(k + 1)The highest degree of z in Numerator and Denominator polynomials of its transfer function H(z) will be, (Assume all initial conditions are zero).a)2 and 3 respectivelyb)3 and 3 respectivelyc)3 and 2 respectivelyd)3 and 4 respectivelyCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for A discrete-time system is given by the equationy(k + 3) = -0.3y(k + 2) + y(k + 1) - 0.5y(k) + 2x(k + 3) - 4x(k + 1)The highest degree of z in Numerator and Denominator polynomials of its transfer function H(z) will be, (Assume all initial conditions are zero).a)2 and 3 respectivelyb)3 and 3 respectivelyc)3 and 2 respectivelyd)3 and 4 respectivelyCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of A discrete-time system is given by the equationy(k + 3) = -0.3y(k + 2) + y(k + 1) - 0.5y(k) + 2x(k + 3) - 4x(k + 1)The highest degree of z in Numerator and Denominator polynomials of its transfer function H(z) will be, (Assume all initial conditions are zero).a)2 and 3 respectivelyb)3 and 3 respectivelyc)3 and 2 respectivelyd)3 and 4 respectivelyCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice A discrete-time system is given by the equationy(k + 3) = -0.3y(k + 2) + y(k + 1) - 0.5y(k) + 2x(k + 3) - 4x(k + 1)The highest degree of z in Numerator and Denominator polynomials of its transfer function H(z) will be, (Assume all initial conditions are zero).a)2 and 3 respectivelyb)3 and 3 respectivelyc)3 and 2 respectivelyd)3 and 4 respectivelyCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice Electronics and Communication Engineering (ECE) tests.
Explore Courses for Electronics and Communication Engineering (ECE) exam

Top Courses for Electronics and Communication Engineering (ECE)

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev