Q$5.$ Consider an analog message $m(t)$ with Fourier transform $M()=P(-1)+P(+1),$ where $P()$ is a triangle centered at $=0$ with height $1$ and base spanning the interval $-1,1($that is$,P()=0$ for $||>1$ and $P()=1-||$ otherwise$).$

a$)$ Assuming AM$-$DSB$-$SC with carrier frequency ${}_c=100,$ plot the Fourier transform of the modulated signal $(t).$

b$)$ Provide the frequency response $H(f)$ of a filter that can be applied to $(t)$ to output AM$-$SSB$.$