mid1_sol_501_Au2011

mid1_sol_501_Au2011 - ECE-501 Introduction to Analog and...

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Unformatted text preview: ECE-501 Introduction to Analog and Digital Communications Autumn 2011 Midterm #1 Oct. 21, 2011 SOLUTIONS with comments and alternatives 1. Problem 1. (a) Large-carrier AM (Observe tone at the carrier frequency; namely, 3 cos(2 100 t ).) To find m ( t ) = m I ( t ) + m Q ( t ), there are several approaches one might take. For ex- ample, consider the bandpass spectrum, then shift to baseband. Recall sin(2 f t ) 1 2 j ( f- f )- 1 2 j ( f + f ). Thus, we have, 1 2 M ( f- 100) = 3 2 ( f- 100) + 1 2 j ( f- 115)- 1 2 j ( f- 85) . Thus, for the complex baseband spectrum, M ( f ), we obtain M ( f ) = 3 ( f ) + 1 j ( f- 15)- 1 j ( f + 15) m ( t ) = 3 + 2 sin(2 15 t ) from which we learn m I ( t ) = 3 + 2 sin(2 15 t ) , m Q ( t ) = 0 Observe 3 max | 2 sin(2 15 t ) | for large carrier. Alternatively, one can directly apply the quadrature demodulator to recover m ( t ). m ( t ) = LPF [3 cos(2 100 t ) + sin(2 115 t )- sin(2 85 t )]2 e- j 2 100 t = LPF [3 cos(2 100 t ) + sin(2 115 t )- sin(2 85 t )]2[cos(2 100...
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This note was uploaded on 11/11/2011 for the course ECE 501 taught by Professor Schniter,p during the Fall '08 term at Ohio State.

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mid1_sol_501_Au2011 - ECE-501 Introduction to Analog and...

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