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

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.


Roger Stafford
on 13 Jan 2013

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
on 13 Jan 2013

Interesting, I didn't know that identity.

Roger Stafford
on 13 Jan 2013

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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1 Answer

Answer by Walter Roberson
on 13 Jan 2013
Edited by Walter Roberson
on 13 Jan 2013


    plot(t, x(t))


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