hi all
im really confused with this question. I'm not really sure how to go about it, hopefully someone here can educate me?
Find the nyquist rate of x(t) = cos(100*pi*t)*sinc(100t) + cos(100*pi*t)
My approach:
Now I know the sinc function equals sinc(100t) = sin(100*pi*t)/(100*pi*t)
so we apply this to our original equation: now we have cos(100*pi*t)*sin(100*pi*t)/(100*pi*t) + cos(100*pi*t)
we can see that the first term "cos(100*pi*t)*sin(100*pi*t)/(100*pi*t)" is a trig identity (1/2)[sin(A-B) + sin(A+B)]
now we can apply this identity to the first term: (1/100*pi*t)(1/2)[sin(100*pi*t - 100*pi*t) + sin(100*pi*t + 100*pi*t)]
Now the entire equation looks like:
(1/100*pi*t)(1/2)[sin(100*pi*t - 100*pi*t) + sin(100*pi*t + 100*pi*t)] + cos(100*pi*t)
Now I really don't know how to finish this problem, I'm not really sure what else to do, can someone please show me how to do this, like through an example or something? I'm really lost...