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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.

6 Comments

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))

Nalini Nadupalli

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1 Answer

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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Walter Roberson

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