Problem $2(75$ points$)$

This problem consists of four parts. In each part we will use a different modulation to transmit the message $m(t)=2cos(w_{m}t)+4cos(3w_{m}t).$ The carrier frequency in all modulations is $f_{c}Hz,$ with $m(t),M(f)m(t)fM(f)0P_{m}m(t)0.$

Sketch the spectrum $(Fourier$ transform$)ofm(t),M(f),$ providing the values $of$ all relevant points $in$ the graph. Define the bandwidth $ofm(t)as$ the the maximum value $off$ where $M(f)0.$

Calculate $P_m,$ the power $ofm(t).$