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

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Nalini Nadupalli
Nalini Nadupalli 2013-1-12
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.
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Roger Stafford
Roger Stafford 2013-1-13
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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Walter Roberson
Walter Roberson 2013-1-13
编辑：Walter Roberson 2013-1-13
Hint:
plot(t, x(t))

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