{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

wss prb3

# wss prb3 - EE 179 Introduction to Communications Winter...

This preview shows pages 1–2. Sign up to view the full content.

EE 179 Introduction to Communications Winter 2011 Homework 5 Due Thursday, Feb 10 4pm (Total: 100 pts.) 1. Random Cosine Signals [15 pts] Given a random process x ( t ) = a cos( ω c t + Θ) where ω c is a constant and a and Θ are independent RVs uniformly distributed in the ranges [ - 1 , 1] and [0 , 2 π , respectively. (a) Sketch the ensemble of this process. (b) Determine x ( t ). (c) Determine R x ( t 1 , t 2 ). (d) Is the process wide-sense stationary? (e) Is the process ergodic? (f) Find the average power P x (that is, its mean square value x 2 ( t )) of the random process x ( t ). 2. Stationarity [10 pts] Let X and Y be statistically independent Gaussian-distributed random variables with zero mean and unit variance. Define the Gaussian process Z ( t ) = X cos(2 πt ) + Y sin(2 πt ) . (a) Determine the joint probability density function of the random variables Z ( t 1 ) and Z ( t 2 ) obtained by observing Z ( t ) at times t 1 and t 2 , respectively. (b) Is the process Z ( t ) stationary? Why? 3. PSD of Random Binary Wave: [15 pts] Let x ( t ) be the infinite pulse train shown below with period T and random time shift τ , where τ is uniformly distributed between [0 , T ]. EE 179 - Introduction to Communications - Spring 2009 Homework 4: Due Thursday 5/7 at 4pm (no late HWs). 1. (20 points) Let x ( t ) be the infinite pulse train shown below with period T and random time shift τ , where τ is uniformly distributed between [0 , T ].

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.
• Spring '11
• Naragipour
• Probability theory, Stochastic process, probability density function, Stationary process, random process

{[ snackBarMessage ]}