1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Discrete Time question

  1. Dec 2, 2005 #1
    w[n] = exp(j*pi*n)

    w[n] = (−1)^n

    Hi, can anyone off hand verify why these two exressions are equal? Thanks
  2. jcsd
  3. Dec 2, 2005 #2
    exp(i * pi * n) = cos(pi * n) + isin(pi * n).

    You figure out the rest.
  4. Dec 2, 2005 #3
    I am assuming n takes on integer values. In which case and expansion of exp(i*pi*n)=cos(pi*n)+i*sin(pi*n). Now for n in Z, sin(pi*n)=0, since: sin(0)=sin(pi)=sin(2pi)=sin(3pi)=...=0. Similarily, cos(pi*n)=(-1)^n, since cos(0)=cos(2pi)=cos(4pi)=..cos(2kpi)=1, and cos(pi)=cos(3*pi)=...cos((2k+1)pi)= -1. Therefore exp(i*pi*n)=(-1)^n for any n in Z.
  5. Dec 2, 2005 #4


    User Avatar
    Science Advisor

    The easiest way is just to write [tex]e^{j \pi n} = (e^{j \pi})^n[/tex] and note that [tex]e^{j \pi} = -1[/tex]
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook