Asked by Nalini Nadupalli
on 12 Jan 2013

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.

Answer by Walter Roberson
on 13 Jan 2013

Edited by Walter Roberson
on 13 Jan 2013

Hint:

plot(t, x(t))

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## 6 Comments

## Walter Roberson (view profile)

Direct link to this comment:https://www.mathworks.com/matlabcentral/answers/58628-how-do-i-plot-it-by-hand-or-in-matlab-if-it-can-be-done-by-both-the-how-to-do#comment_122200

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 (view profile)

Direct link to this comment:https://www.mathworks.com/matlabcentral/answers/58628-how-do-i-plot-it-by-hand-or-in-matlab-if-it-can-be-done-by-both-the-how-to-do#comment_122201

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

## Nalini Nadupalli (view profile)

Direct link to this comment:https://www.mathworks.com/matlabcentral/answers/58628-how-do-i-plot-it-by-hand-or-in-matlab-if-it-can-be-done-by-both-the-how-to-do#comment_122230

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 (view profile)

Direct link to this comment:https://www.mathworks.com/matlabcentral/answers/58628-how-do-i-plot-it-by-hand-or-in-matlab-if-it-can-be-done-by-both-the-how-to-do#comment_122239

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

## Walter Roberson (view profile)

Direct link to this comment:https://www.mathworks.com/matlabcentral/answers/58628-how-do-i-plot-it-by-hand-or-in-matlab-if-it-can-be-done-by-both-the-how-to-do#comment_122243

Interesting, I didn't know that identity.

## Roger Stafford (view profile)

Direct link to this comment:https://www.mathworks.com/matlabcentral/answers/58628-how-do-i-plot-it-by-hand-or-in-matlab-if-it-can-be-done-by-both-the-how-to-do#comment_122255

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))

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