Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
229 views
in General by (115k points)
closed by
Consider a random process \(\rm X(t) = 3V(t) − 8\), where (t) is a zero mean stationary random process with autocorrelation \(\rm R_{V}(\tau)=4e^{-5\left|\tau\right|}\). The power in \(\rm X(t)\) is ________

1 Answer

0 votes
by (152k points)
selected by
 
Best answer

Concept:

ACF is defined as:

Rx(τ) = E[x(t) x(t + τ)] = E[x(t) x(t - τ)]

Properties of ACF:

1. Rx(-τ) = Rx (τ)

2. Rx (0) = E [x2(t)] = Power of x(t)

Calculation:

Given:

x(t) = 3 V(t) – 8,  Rv(τ) = 4e-5|τ|

E [V(t)] = 0

We know that,

Power of x(t) = E[x2(t)]

= E[9V2(t) + 64 – 48 E[V(t)]]

= 9E [V2(t)] + 64 – 48 E[V(t)]

Now,

E[V2(t)] = Rv(0) = 4

So,

Power of x(t) = (9 × 4) + 64 – 0

Power of x(t) = 100  

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...