m,(1) ;(1) H(f) Xour (1) cos(2# f,J) cos(2.rf,1) m,(1) |H(f)
Using the orthogonality of sine and cosine makes it possible to transmit and
receive two different signals simultaneously on the same carrier frequency. A scheme to do
this, known as quadrature multiplexing or quadrature amplitude modulation (QAM), is shown in Figure
a) Write down the expression for ( ) QAM x t ?
b) Derive the two expressions for the outputs 1 y t( ) and 2 y t( ) after the demodulator and
low pass filter.
c) Consider the situation when the receiver is not exactly synchronised with the
transmitter, thus the demodulator at the receiver has a slight frequency shift
cos(2 ( ) ) c π f ft + ∆ where ??∆ ≪ ????. Derive the two expressions for the outputs 1 y t( )
and 2 y t( ) after the demodulator and low pass filter for this case (Consider only the
noise free situation).
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