Q1) [60p] Given the following message and carrier signal m(t) = cos 2000nt + 2cos 6000лt + cos 10000πt c(t) = 20 cos 320000πt The signal is passed through following nonlinear device and a subsequent filter to generate DSB-AM signal. The nonlinear device has the input-output relation y(t) = x²(t) + 10x(t). y(t) u(t) m(t). Non-Linear Device Filter c(t) a) Determine y(t). b) Determine type of filter (BPF, HPF, LPF) and the bandwidth to obtain a DSB-AM signal (Conventional AM) c) What is the modulation index? d) Determine power of m(t), u(t), and the ratio of power in side bands to carrier. e) Assume that modulation signal u(t) is going to be demodulated by an envelope detector. The resistor is selected as R = 1 K. What is the minimum and maximum value of capacitor for a good detector. Q2) [40p] Given the following message and carrier signal m(t) = cos 2000πt + 2cos 6000πt + cos 10000πt c(t) 20 cos 320000лt a) Determine the Hilbert transform of m(t). b) Determine the Single Side Band (SSB) AM signal usSB (t) which uses upper sideband. c) Plot the spectrum USSB (f) of USSB (t).