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!

Help with Eulers relation in Fourier analysis

  1. Apr 14, 2013 #1
    Hi I'm doing fourier analysis in my signals and system course and i'm looking at the solution to one basic problem but I'm having trouble understanding one step
    awe6sNa.png
    Can anyone explain to me why
    ViStWY6.png
    becomes
    RqMZI6O.png
    From Eulers formula: http://i.imgur.com/1LtTiKX.png

    for example the Cosine in my problem. I thought the "twos" would cancel each other but instead becomes 4 and simular for the sine.
     
  2. jcsd
  3. Apr 14, 2013 #2

    CompuChip

    User Avatar
    Science Advisor
    Homework Helper

    If
    [tex]\cos z = \frac{e^{jz} + e^{-jz}}{2}[/tex]
    then multiply everything by 2 to get
    [tex]2 \cos z = e^{jz} + e^{-jz}[/tex]

    Or you can use the identity
    [tex]e^{jz} = \cos(z) + j \sin(z)[/tex]
    and also immediately get
    [tex]e^{jz} + e^{-jz} = \cos(z) + j \sin(z) + \cos(z) - j \sin(z) = 2 \cos(z)[/tex]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Help with Eulers relation in Fourier analysis
  1. Fourier Analysis (Replies: 1)

Loading...