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mid1_sol_501_Au2011

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

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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 π 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 πf 0 t ) 1 2 j δ ( f - f 0 ) - 1 2 j δ ( f + f 0 ). Thus, we have, 1 2 ˜ M ( f - 100) = 3 2 δ ( f - 100) + 1 2 j δ ( f - 115) - 1 2 j δ ( f - 85) . Thus, for the complex baseband spectrum, ˜ M ( f ), we obtain ˜ M ( f ) = 3 δ ( f ) + 1 j δ ( f - 15) - 1 j δ ( f + 15) ˜ m ( t ) = 3 + 2 sin(2 π 15 t ) from which we learn m I ( t ) = 3 + 2 sin(2 π 15 t ) , m Q ( t ) = 0 Observe 3 max | 2 sin(2 π 15 t ) | for “large carrier.” Alternatively, one can directly apply the quadrature demodulator to recover ˜ m ( t ). ˜ m ( t ) = LPF [3 cos(2 π 100 t ) + sin(2 π 115 t ) - sin(2 π 85 t )]2 e - j 2 π 100 t = LPF [3 cos(2 π 100 t ) + sin(2 π 115 t ) - sin(2 π 85 t )]2[cos(2 π 100 t ) - sin(2 π 100 t )] = LPF [3 cos(0) + dbl + j 3 sin(0) + j dbl + ...
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