EECE 340 Midterm, Spring 2008

AMERICAN UNIVERSITY OF BEIRUT ELECTRICAL AND COMPUTER ENGINEERING DEPARTMENT __________________________________________________________ EECE 440 SIGNALS AND SYSTEMS Summer 2005 Prof. Kabalan Midterm Exam July 25, 2005 __________________________________________________________ __________________________________________________________ NAME: ID NUMBER: __________________________________________________________ INSTRUCTIONS: 1. Open-Book Exam 2. Duration: Two Hours 3. Provide your answers on the question sheet. 4. 15 pages, 50 pts 5. On this sheet, write your name and ID # in the provided space. _________________________________________________________ Problem 1 (3 pts) Determine whether or not the following signal f(t)=4u(t)+2sin(3t) is periodic. If the signal is periodic, determine its fundamental period. Problem 2 (4 pts) EECE 440-Midterm Exam 1/15 The input-output relationship of a system is given by: a. Is this system linear? Justify your answer b. Is this system time-invariant? Justify your answer. Problem 3 (3 pts) Consider a system whose input-output relationship is given by: EECE 440-Midterm Exam 2/15 a. Is this system linear? Justify your answer. b. Is the system causal? Justify your answer. c. Is the system memory-less? Justify your answer. EECE 440-Midterm Exam 3/15 Problem 4 (2 pts) The response of an LTI system to a unit step input x(t)= 4u(t) is y(t)= . What is the response to an input of ? EECE 440-Midterm Exam 4/15 Problem 5 (3 pts) The block diagram representation of an LTI system is shown below. Determine the transfer function of this system. EECE 440-Midterm Exam + + + + + + + R(s) C(s) 5/15 Problem 6 (3 pts) The open loop transfer function of a unity feedback control is given by: Check for system stability by determining the number of poles in each half of the complex plane. EECE 440-Midterm Exam 6/15 Problem 7 (3 pts) The open-loop transfer function of a unity-feedback control system is given by: Determine the range of K for which this system is stable. Problem 8 (4 pts) EECE 440-Midterm Exam 7/15 The dynamic equations of a linear time-invariant system whose output is y(t) and input r(t) are given by: Determine the Differential equation representing this system. Problem 9 (3 pts) EECE 440-Midterm Exam 8/15 An AM transmitter is tested as follows: With no audio input, the wattmeter reads 200W average power. With an audio input signal of 10V peak at 1 KHz, the Wattmeter reads 250W. What is the modulation index? EECE 440-Midterm Exam 9/15 Problem 10 (3 pts) Consider a single-tone modulated DSB-LC signal Assume that s(t) is over modulated and that the envelope of s(t) has two maxima. The first is 1.5 and the second is . Determine the percentage modulation of s(t). Problem 11 (4 pts) EECE 440-Midterm Exam 10/15 Consider a DSB-LC signal where the message m(t) is given by: The DSB-LC signal is inputted to an ideal band-pass filter followed by an envelope detector. The ideal band-pass filter is tuned to the frequency of the carrier with a bandwidth that passes 7 Hz on either side of this frequency. a. Find the output of the filter. b. Find the output of the envelope detector. Problem 12 (4 pts) Consider an information signal: EECE 440-Midterm Exam 11/15 . a. Determine the Hilbert Transform of s(t) (1 pt) b. Determine be the pre-envelope of the signal s(t). (1 pt) c. Determine the ratio of the average power of s(t) to the average power of the pre-envelope of s(t). (2 pts) Problem 13 (3 pts) Consider an AM (DSB-LC) signal and an FM signal given by: EECE 440-Midterm Exam 12/15 For both signals, the message signal is a single-tone of frequency Hz. The maximum frequency deviation of the FM signal is set to five times the bandwidth of the AM signal. The magnitudes of the side frequency components spaced  Hz from carrier in both AM and FM signals are equal. Determine the modulation index of the FM signal. Problem 14 (4 pts) Consider the following Frequency modulated signal s(t) EECE 440-Midterm Exam 13/15 a. Determine the carrier frequency in rad/sec. b. Determine the maximum frequency deviation in rad/sec. Problem 15 (4 pts) Consider a single tone FM signal with amplitude =12 Volts, frequency =6 KHz, and modulation index β = 1.5. Determine the ratio of the average power of the frequency components of this FM signal contained EECE 440-Midterm Exam 14/15 within its bandwidth to the total signal average power. Use Carson’s rule for bandwidth computation. EECE 440-Midterm Exam 15/15