ECEN3713 Network Analysis Lecture #25 11 April 2006 Dr. George Scheets Exam 2 Results: Hi = 89, Lo = 30, Ave. = Standard Deviation = Quiz 8 Results: Hi = 9, Lo = 2, Ave. = 4.42 Standard Deviation = 2.56 n Read Chapter n Problems: 15.26, 15.28, n Thursday's Quiz u Active Filters Thursday's Assignment Problems: 15.58, 16.1, 16,2

ECEN3713 Network Analysis Lecture #27 18 April 2006 Dr. George Scheets n Read Chapter n Problems: 16.11, 16.13, n Thursday's Quiz u Chapter 16 n Final Exam, Thursday, 4 May, u Comprehensive, Open Book & Notes Thursday's Assignment Problems: 16.23, 16.24, 16.29, 16.33

ECEN3713 Network Analysis Lecture #29 25 April 2006 Dr. George Scheets Quiz 10 Results: Hi = 10, Lo = 3, Ave. = 5.65 Standard Deviation = 2.47 n Problems: 16.34, 16.35, 16.41, n Final Exam u 2:00-3:50pm, Thursday, 4 May n Office Hours u Wednesday Office Hours: Thursday Office Hours: ,

ECEN3713 Network Analysis Lecture #30 27 April 2006 Dr. George Scheets Final Exam u 2:00-3:50pm, Thursday, 4 May n Office Hours u Wednesday Office Hours: Thursday Office Hours: ,

How do S-Domain poles & zeroes affect frequency domain plots? n Real Pole u Causes |H(s)| to "blow up" u Causes |H(jω)| to break down n Real Zero u Causes |H(s)| to be = 0 u Causes |H(jω)| to break up n Complex Conjugate Pole Pairs u Cause |H(s)| to "blow up" in two symmetrical places u Cause |H(jω)| to have bulges

Single Real Pole, Two Real Poles 1/(s+3), 1/(s+3) 2 |H(ω)|

Single Real Pole, Two Real Poles 1/(s+3), 3/(s+3) 2 |H(ω)| Note: 2 nd order system has sharper roll-off. Also, 3 dB break point has moved.

Complex Conjugate Poles, |real| = 0 1/(s ) = 1/[(s + j10)(s – j10)] |H(ω)|

Complex Conjugate Poles, |real| > 0 1/(s 2 + 4s + 104) = 1/[(s j10)(s + 2 – j10)] |H(ω)|

Complex Conjugate Poles, |real| > 0 1/(s s + 125) = 1/[(s j10)(s + 5 – j10)] |H(ω)|

Correlation n Tells how "alike" x(t) and y(t) are n If evaluates positive u if x(t1) is positive, y(t1) tends to be positive t1 an arbitrary time u x(t) and y(t) are similar, i.e. there is a lot of y(t) in x(t) x(t) y(t) dt

Correlation n If evaluates negative u if x(t1) is positive, y(t1) tends to be negative & vice-versa u x(t) and y(t) are similar but opposites n If evaluates = 0 u x(t) & y(t) are not related (uncorrelated) no predictability x(t) y(t) dt

Laplace Transform F(s) = f(t) e -st dt 0-0- ∞ n F(3) tells how alike f(t) and e -3t are u Over the time interval 0- to infinity

Fourier Transform F(ω) = f(t) e -jωt dt - ∞ ∞ n F(3) tells how alike f(t) and e -j3t are u Over the time interval - u Over the time interval - ∞ to +∞

Fourier Series a n = 2/T f(t) cos(nω o t) dt 0 n a 3 tells how alike f(t) and n a 3 tells how alike f(t) and cos(3ω o t) are u Over one period, T u 1/T = average u 2 = scaling factor to get power correct T