hw04su08

# hw04su08 - GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of...

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GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of ELECTRICAL and COMPUTER ENGINEERING ECE 2025 Summer 2008 Problem Set #4 Assigned: Week of 9-Jun-08 Due Date: 16/17-Jun-08 = Please check the “Announcements” often on T-square. All official course an- nouncements are posted there. ALL of the STARRED problems will have to be turned in for grading. A solution to the starred problems will be posted to the web. Some problems have solutions similar to those found on the CD-ROM. Your homework is due in recitation at the beginning of class. After the beginning of your assigned recitation time, the homework is considered late and will be given a zero. PROBLEM 4.1 *: - Ideal C-to-D Converter Ideal D-to-C Converter - - x ( t ) x [ n ] y ( t ) 6 T s = 1 /f si 6 T s = 1 /f so (a) Suppose that the input x ( t ) is given by x ( t ) = 8 + 4 cos(2 π (300) t - 3 π/ 7) + 10 cos(2 π (700) t + 2 π/ 3) + 6 cos(2 π (1000) t - 5 π/ 9) Determine the spectrum for x [ n ] for - π ˆ ω π when f si = 800 samples/sec. Make a plot for your answer, making sure to label the frequency, amplitude and phase of each spectral component. (b) Using the discrete-time spectrum from part (a), find the analog output y ( t ) when the sampling rate of the D-to-C converter is f so = 800 Hz. Express your answer the same way we expressed x ( t ) above, i.e. in terms of cosines.

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