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.

[Walter Roberson]

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

[Azzi Abdelmalek]

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

[Nalini Nadupalli]

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.

[Roger Stafford]

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)

[Walter Roberson]

Interesting, I didn't know that identity.

[Roger Stafford]

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

[Walter Roberson]

Hint:

    plot(t, x(t))