Previous Year Question
The power of the signal (–1)n u[n] is
Correct answer: B
Explanation
For n≥0, |(−1)^n|²=1; for n<0 the unit step makes the signal zero. Using the standard symmetric average from −N to N gives P=lim(N+1)/(2N+1)=1/2=0.5. Thus option B is correct.
Formula
P=lim[N→∞](1/(2N+1))Σ|x[n]|²=1/2
Step-by-step solution
![Power of (−1)^n u[n] explanatory diagram](https://sarkariresultout.com/wp-content/uploads/2026/09/sro-pyq-b9575550ce719868ff29cfe9.webp)
Correct Answer
B — 0.5
Concept and Reasoning
For n≥0, |(−1)^n|²=1; for n<0 the unit step makes the signal zero. Using the standard symmetric average from −N to N gives P=lim(N+1)/(2N+1)=1/2=0.5. Thus option B is correct.
Calculation / Key Relation
P=lim[N→∞](1/(2N+1))Σ|x[n]|²=1/2
Exam Takeaway
The unit step makes only about half of the symmetric time axis nonzero.
Common Mistake
Do not answer 1 merely because the nonzero samples have unit magnitude.
Common mistake
Do not answer 1 merely because the nonzero samples have unit magnitude.
Exam tip
The unit step makes only about half of the symmetric time axis nonzero.
Quick method
The unit step makes only about half of the symmetric time axis nonzero.