Name:

Problem	Points	Score	
1a	10		
1b	10		
2a	10		
2b	10		
2c	10		
3a	10		
3b	10		
3c	10		
3d	10		
3e	10		
Total	100		

Notes:

1.	The exam is closed books/closed notes - except for one page of notes.

2.	Please show ALL work. Incorrect answers with no supporting explanations or work will be given no partial credit.

3.	Please indicate clearly your answer to the problem. If I can’t read it (and I am the judge of legibility), it is wrong. If I can’t follow your solution (and I get lost easily), it is wrong. All things being equal, neat and legible work will get the higher grade:)

Problem No. 1: Show the following properties of the Fourier transform for real signals:

(a) 

(b) 

Problem No. 2: For the following two signals:
(a)	Plot the magnitude spectrum of :

(b)	Plot the magnitude spectrum of :

(c)			Compare and contrast these plots (note that you can answer this question correctly without getting the correct answers for (a) and (b).

Problem No. 3: For the following system,
(a) Find :

(b) Find :

(c) For the circuit shown, construct the Bode magnitude plot.

(d) How many poles and zeros does the system have?

(e) Using concepts introduced in Chaps. 4 - 6, determine the stability of the system.