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Unformatted text preview: GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of ELECTRICAL and COMPUTER ENGINEERING ECE 2025 Summer 2010 Problem Set #9 Assigned: Week of 20-Jul-10 Due Date: 26/27-Jul-10 Please check the T-square Announcements daily. All official course announcements will be posted there. ALL of the STARRED problems should be turned in for grading. PROBLEM 9.1 : Problem 11.6 on p. 342 of Signal Processing First . PROBLEM 9.2 : Problem 11-8 on p. 343 of Signal Processing First . PROBLEM 9.3 : (a) Problem 12.1 on p. 381 of Signal Processing First . (b) Problem 12.2 on p. 381 of Signal Processing First . PROBLEM 9.4 : (a) Problem 12.4 on p. 381-382 of Signal Processing First . Try to think graphically as much as possible; you will find that more convenient than wrangling equations. (b) Problem 12.5 on p. 382 of Signal Processing First . PROBLEM 9.5 *: The system in the dashed box below is called a quadrature modulation system . It is a method of sending two bandlimited signals in the same frequency band in a way that can be uniquely unscrambled. a45 a45 a54 a54 a54 a63 a45 a45 a54 LTI System H ( j ) a45 a45 + + x 2 ( t ) x 1 ( t ) cos c t sin c t w ( t ) w ( t ) y ( t ) cos c t v ( t ) Quadrature Modulator Demodulator = Mixer, then Filter w ( t ) = x 1 ( t )cos c t + x 2 ( t )sin c t Assume that both input signals are bandlimited with highest frequency m ; i.e., X 1 ( j ) = 0 for | | m and X 2 ( j ) = 0 for | | m , where c m . (a) Determine an expression for the Fourier transform W ( j ) in terms of X 1 ( j ) and X 2 ( j ). Make a sketch of W ( j ). Assume simple (typical) shapes (each different) for the bandlim- ited Fourier transforms X 1 ( j ) and X 2 ( j ), and use them in making your sketch of W ( j )....
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