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Periodic Complex exponential signal

  1. Oct 14, 2014 #1
    hello guys ..
    first of all , iam not sure that i should type this thread here . so excuse me for that

    in this problem i can understand the part untill it's said that w=0 then x(t)=1, which is periodic for any value of T
    but i can't understand the part after that in the case of w is not equal to zero
    so help me with this please :)
    Thx guys

    MVHb9lE.png
     
  2. jcsd
  3. Oct 14, 2014 #2

    DrClaude

    User Avatar

    Staff: Mentor

    Perhaps Euler's formula will be of help:
    $$
    e^{i \omega_0 T} = \cos(\omega_0 T) + i \sin (\omega_0 T)
    $$
     
  4. Oct 14, 2014 #3
    okay , i know Euler's formula but i can't understand " wt=m*2*pi " or "T=m*(2pi/w) m=positive integer"

    how did this part was given ??
     
  5. Oct 14, 2014 #4

    DrClaude

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    Staff: Mentor

    You want ##
    e^{i \omega_0 T} = \cos(\omega_0 T) + i \sin (\omega_0 T) = 1
    ##, meaning that ##\cos(\omega_0 T)=1## and ##\sin (\omega_0 T)=0##. What are the values of ##\omega_0 T## for which these equalities hold?
     
  6. Oct 14, 2014 #5
    omg , now i understand , we need cos(wT) to be always 1 , so cos (2*pi) and (4*pi) and so on , yaaaayyyyy :D
    Thx man for help :)
     
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