Two real baseband signals x (t) and x2(t) are modulated using the following modulator before transmission, Assume that there is no power loss or noise in the channel.. 24Hz (X) x (1) X (t) Y (t) cos(2nfit) (40k (X) 1 cos(2nft) Y/ (t) Cos (20k Tit) lok 117 y(t) = y (t) + y (1) Y (jw) Modulator The corresponding frequency spectrum Y(jw) for positive values of w is shown below. 840km Y (jw) channel 850km 870km Receiver 800km a) (1) What is the value of (in kHz) ? b) (1) What is the value of f (in kHz) ? c) (1) What is the unilateral bandwidth (in kHz) of signal x(t) ? d) (1) What is the unilateral bandwidth (in kHz) of signal x(t) ? e) (4) Show the detailed design of the receiver for recovering x(t) or x (t) by sketching a block diagram. + X (1) TCS (4-40k Ti) + SLW +4.0 kn ]] co (rad/s) or f) (4) You are allocated the radio spectrum from 600 kHz to 700 kHz for sending multiple baseband signals using amplitude modulation and frequency division multiplexing (FDM). Assume that all the baseband signals have the same unilateral bandwidth of 10 kHz, how many baseband signals can be sent at the same time? Briefly explain your answer, and list one possible set of carrier frequencies that you can use for sending the baseband signals. Note that I/Q modulation is used in digital communication. The figure shown below is en 1/0 modulator (X) x(1) %, (1) imaginary A J 0010 0011 g) (2) Describe how the signals generated by Oscillator 1 and Oscillator 2 are related. h) (2) Assume that 16-QAM (Quadrature Amplitude Modulation) with signal constellation as shown below is used to transmit bits. How many different values can x,(t) or xo(t) take for each symbol? Gray coded hit mapping for 10-1 0001 0000 Oscillator 1 Oscillator 2 0110 y, (t) 0111 0101 Yq(t) 0100 1 (+) 0 real 1110 1111 1101 1100 1 2 y(t) = y(t) + y(t) 1010 1011 1001 1000 3 In OFDM (Orthogonal Frequency Division Multiplexing), a very large number of subcarriers are used to transmit many bits per symbol. i) (2) Name two communication systems where OFDM is used. 1) (2) Briefly explain why we have to perform Fourier analysis of the received signal in OFDM.