A DSB-SC signal is modulated by m(t) = cos 1t + 2 cos 21t , where 1=2f1

A DSB-SC signal is modulated by m(t) = cos ω1t + 2 cos 2ω1t , where ω1=2πf1 , f1=500Hz and the unmodulated carrier amplitude and frequency are 1 volt and 1 MHz respectively. 

a) Write the expression of this modulated signal. 

b) Sketch the spectrum of this modulated signal. 

c) Evaluate the transmitted power and efficiency. 

d) If  the upper side band only is sent, write an expression for the resultant SSB-SC modulated signal. 

e) IF a DSB-LC is sent, write its mathematical expression. Can you use an envelope detector in this case for demodulation? If yes sketch the demodulator, if no explain why and sketch a suitable demodulator.