How do I plot it? by hand or in matlab? if it can be done by both the how to do?

 x(t)=cos(2π30t)+cos(2π70t+π) is sampled at 100 SAMPLE SECOND.

 (a) Show algebraically (by substituting t= n/100 ) that the sampled signal is 0!
 (b) Plot the spectrum of the sampled signal. Show all of the components cancel.

To do the first part by using MATLAB you would need to use the symbolic toolbox and do a bunch of manual algebraic manipulation.

If this is a homework, what have you done so far?

I have done the first part, for which i am unsure of the the method by which I have proved and the second part is where I am stuck at.

Hint on part (a) if you are still unsure: You need the identity

 cos(A) + cos(B) = 2*cos((A+B)/2)*cos((A-B)/2)

Interesting, I didn't know that identity.

It's easy to prove using the two formulas for the cosine of the sum and the difference between two angles:

cos(A) = cos((A+B)/2+(A-B)/2) = cos((A+B)/2)*cos((A-B)/2)) - sin((A+B)/2)*sin((A-B)/2))

cos(B) = cos((A+B)/2-(A-B)/2) = cos((A+B)/2)*cos((A-B)/2)) + sin((A+B)/2)*sin((A-B)/2))

Adding these gives:

cos(A) + cos(B) = 2*cos((A+B)/2)*cos((A-B)/2))

Answer 1

Hint:

    plot(t, x(t))