Q$3)(25\%)$ Find and consider the spectrums $W(f)$ of the following signals $w(t).$ Find the lowest sampling frequency $f_s$ of $w(t)($it is also called the Nyquist rate$)$ so that after sampling operation on $w(t)$ the analog signal can be recovered by low pass filtering of the sampled signal without aliasing.

a$)w(t)=10cos(200t)cos(400t).$

b$)w(t)=10+10co{s}^2(400t).$

c$)w(t)=200Sa(200t).$

d$)w(t)=[200Sa(200t)]cos(200t).$

e$)w(t)=[10cos(100t)+10cos(400t)]**[200Sa(200t)]$ Where $*$ symbol denotes convolution $2cosxcosy=cos(x-y)+cos(x+y),2co{s}^{2}x=1+cos2x$