{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# Prob2 - ECE 1520 Data Communications Fall 2011 Problem Set...

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

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.

Unformatted text preview: ECE 1520 Data Communications Fall 2011 Problem Set 2 Due in class, Wednesday, Oct. 5th, 2011. 1. I had wanted to show this in class, but then didn’t want to take the time: Consider a lowpass Gaussian WSS random process, X ( t ) with bandwidth W and power spectral density S x ( f ) = braceleftbigg 1 | f | ≤ W | f | > W Now, define a discrete random process X [ n ] as a sampled version of X ( t ), i.e., X [ n ] = X ( nT s ) where T s is the sampling period. (a) Is the discrete process WSS, i.e., is E [ X [ n ] X * [ n + m ]] = R x [ m ] (independent of the value of n )? Prove your answer. If ‘yes’, find the relationship between R x [ m ] and the original autocorrelation function R x ( τ ). (b) Show that if T s just meets Nyquist criterion, i.e., T s = 1 / 2 W , the samples are i.i.d. Gaussian random variables. 2. Q6.3 from the text: The alphabet of a DMS, X , is { a 1 ,a 2 ,...,a n } with correspond- ing probabilities { p 1 ,p 2 ,... ,p n } . Show that H ( X ) is maximized when p...
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

Prob2 - ECE 1520 Data Communications Fall 2011 Problem Set...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online