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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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 comentarios
Roger Stafford
Roger Stafford el 13 de En. de 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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Walter Roberson
Walter Roberson el 13 de En. de 2013
Editada: Walter Roberson el 13 de En. de 2013
Hint:
plot(t, x(t))

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