EE 567 Homework Set #3
Due Date:
Friday, September 25 @ 5:00p in EE 567 drop box near EEB 104
Text:
Modern Digital and Analog Communication Systems
Problems:
Problem 8.16
Problem 8.17
Problem 8.114
Problem 8.116
Problem 8.210
Problem 8.61
Problem 9.15
Problem 9.23
Problem 9.33
Problem 9.42
Problem 9.72
Computer Problems:
Problem 1:
Autocorrelation Function and Power Spectrum
The objective of this problem is to compute the autocorrelation and the
power spectrum of a sequence of random variables.
1. Generate a discretetime sequence x
n
of N = 1000 statistically
independent and identically distributed random variables, which are
selected from a uniform distribution over the interval (1/2, 1/2).
The estimate of the autocorrelation of the sequence x
n
is defined as
ܴ
ሺ݉ሻ ൌ
ە
ۖ
۔
ۖ
ۓ
1
ܰ െ ݉
ݔ
ݔ
ା
, ݉ ൌ 0,1, … ܯ
ேି
ୀଵ
1
ܰ െ ݉
ݔ
ݔ
ା
, ݉ ൌ െ1, െ2, … െ ܯ
ே
ୀ
ܵ
ሺ݂ሻ ൌ
ܴ
ሺ݉ሻ
ெ
ୀିெ
݁
ି
ଶగ
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 Fall '07
 WEBER
 Probability theory, power spectrum, sequence Xn

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