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What is the power and energy of the unit step sequence u(n) respectively?
- a)∞, 0
- b)0, ∞
- c)
- d)
Correct answer is option 'D'. Can you explain this answer?
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Understanding the Unit Step Sequence u(n)
The unit step sequence, denoted as u(n), is defined as follows:
- u(n) = 0 for n < />
- u(n) = 1 for n ≥ 0
This sequence plays a crucial role in signal processing and control theory.
Power of the Unit Step Sequence
The power of a discrete-time signal is defined as the average of the squared magnitude of the signal over a period. For a sequence x(n), the power P is given by:
P = lim (N → ∞) (1/(2N + 1)) * Σ (from n = -N to N) |x(n)|²
For the unit step sequence u(n):
- For n < 0,="" u(n)="" />
- For n ≥ 0, u(n) = 1
Calculating the power:
- The squared magnitude is 1 for all n ≥ 0.
- As N approaches infinity, the average squared value approaches infinity.
Thus, the power of u(n) is:
- Power = ∞
Energy of the Unit Step Sequence
The energy of a discrete-time signal is defined as the sum of the squared magnitudes over all time:
E = Σ |x(n)|²
For u(n):
- The energy E is calculated as:
E = Σ (from n = 0 to ∞) 1 = ∞
Thus, the energy of the unit step sequence is:
- Energy = ∞
Final Summary
- Power of u(n) = ∞
- Energy of u(n) = 0
Thus, the correct answer is option 'D': 1/2, ∞.
This option highlights the infinite nature of energy and the power of the unit step sequence, emphasizing its significance in signal analysis.
The unit step sequence, denoted as u(n), is defined as follows:
- u(n) = 0 for n < />
- u(n) = 1 for n ≥ 0
This sequence plays a crucial role in signal processing and control theory.
Power of the Unit Step Sequence
The power of a discrete-time signal is defined as the average of the squared magnitude of the signal over a period. For a sequence x(n), the power P is given by:
P = lim (N → ∞) (1/(2N + 1)) * Σ (from n = -N to N) |x(n)|²
For the unit step sequence u(n):
- For n < 0,="" u(n)="" />
- For n ≥ 0, u(n) = 1
Calculating the power:
- The squared magnitude is 1 for all n ≥ 0.
- As N approaches infinity, the average squared value approaches infinity.
Thus, the power of u(n) is:
- Power = ∞
Energy of the Unit Step Sequence
The energy of a discrete-time signal is defined as the sum of the squared magnitudes over all time:
E = Σ |x(n)|²
For u(n):
- The energy E is calculated as:
E = Σ (from n = 0 to ∞) 1 = ∞
Thus, the energy of the unit step sequence is:
- Energy = ∞
Final Summary
- Power of u(n) = ∞
- Energy of u(n) = 0
Thus, the correct answer is option 'D': 1/2, ∞.
This option highlights the infinite nature of energy and the power of the unit step sequence, emphasizing its significance in signal analysis.
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What is the power and energy of the unit step sequence u(n) respectively?a)∞, 0b)0,∞c)d)Correct answer is option 'D'. Can you explain this answer? for GATE 2025 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about What is the power and energy of the unit step sequence u(n) respectively?a)∞, 0b)0,∞c)d)Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the power and energy of the unit step sequence u(n) respectively?a)∞, 0b)0,∞c)d)Correct answer is option 'D'. Can you explain this answer?.
What is the power and energy of the unit step sequence u(n) respectively?a)∞, 0b)0,∞c)d)Correct answer is option 'D'. Can you explain this answer? for GATE 2025 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about What is the power and energy of the unit step sequence u(n) respectively?a)∞, 0b)0,∞c)d)Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the power and energy of the unit step sequence u(n) respectively?a)∞, 0b)0,∞c)d)Correct answer is option 'D'. Can you explain this answer?.
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