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Unformatted text preview: ECE-501 Introduction to Analog and Digital Communications Autumn 2011 Homework #6 Nov. 4, 2011 HOMEWORK ASSIGNMENT #6 Due Mon. Nov. 14, 2011 (in class) Problems: 1. Consider the quadrature modulator/demodulator system (with trivial noiseless channel) illustrated below. As usual, define ˜ m ( t ) = m I ( t ) + jm Q ( t ) and ˜ v ( t ) = v I ( t ) + jv Q ( t ). Observe the frequency f c + f and phase φ of the oscillator at the demodulator. m I ( t ) m Q ( t ) × × × × ∼ ∼ − − + v I ( t ) v Q ( t ) LPF LPF cos(2 πf c t ) sin(2 πf c t ) 2 cos(2 π ( f c + f ) t + φ ) 2 sin(2 π ( f c + f ) t + φ ) s ( t ) = r ( t ) Let the message signal be given by m I ( t ) = 1 , m Q ( t ) = 0 ( Hint : A complex baseband view of modulation/demodulation may simplify your analysis.) (a) Show that | ˜ v ( t ) | 2 = v 2 I ( t ) + v 2 Q ( t ) = 1. (b) With the angle of ˜ v ( t ), ∠ ˜ v ( t ), as shown, solve for φ and f ....
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