EECE 200 Homework 1, Fall 2011

American University of Beirut Faculty of Engineering and Architecture Department of Electrical and Computer Engineering EECE200 – Introduction to Engineering– Fall 2011-­‐2012 Homework 1 Problem 1 [30 points] Answer the following questions for the plot below. The amplitude is in volts and the time is in seconds a. Find the amplitude of y1, y2, and y3 [3 points]. b. Find the frequency, period, and angular frequency ω of each of the signals y1, y2, and y3. (Do not forget the units) [9 points]. c. Which signal has the highest frequency [1 point]? d. If y1, y2, and y3 can be written in the form of y(t)=A sin(wt+θ), find the corresponding phase shift θ1, θ2, and θ3 of the three signals in radians and then in degrees[12 points]. • Show your analysis. • Validate the calculated phases by finding the value of the signal at t=0 e. Sketch the frequency domain of the above signals [5 points]. Problem 2 [10 points] a. Name one of the FM stations and state its frequency. Validate that it is within the FM dedicated bandwidth [3 points]. b. How many stations can the AM dedicated bandwidth afford in Lebanon? Verify [3 points] c. Is the bandwidth of TV stations bigger than FM stations? Why? [2 points] d. Is the bandwidth of black and white TV station bigger than that of a color TV station? Why? [2 points] Problem 3 [25 points] a. What are the dimensions of this image in pixels? [2 points] b. How many bits are needed to represent one pixel? Verify. Write the binary representation of each grey level [10 points]. c. Show the matrix representation of this image. The matrix entries should be in decimal numbers. [8 points] d. If the image is part of a movie that is playing at a rate of 30 frames (pictures) per second; what would the size of the file be in mega bytes if I record on my computer 2.5 minutes of the movie? [5 points] Problem 4 [35 points] a. Use the algorithm described in class to calculate the decimal equivalent of 10011101.0111012. Show all steps [9 points]. b. Use the algorithm described in class to calculate the binary equivalent of 485.2310. Show all steps in details [9 points]. c. Convert 15748 from octal to binary representation. Show all steps. [4 points] d. Convert 1000111112 from binary to hexadecimal representation. Show all steps. [4 points] e. Convert 1C8B16 from hexadecimal to decimal representation. Show all steps. [9 points]