Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I Q about Fourier Coefficient Derivation

  1. Mar 30, 2016 #1
    For the calculation of cn u have to multiply the equation

    ∑ cn * ejnx
    by
    e-jmx

    what is the reason for this? in my textbook it says nothing about it and on some sites it just said "without justification"
    i guess what im asking is why does this do what we want?
    ps: how do u properly make equations here?
     
  2. jcsd
  3. Mar 30, 2016 #2

    blue_leaf77

    User Avatar
    Science Advisor
    Homework Helper

    It's not just multiplication, but you also have to integrate the resulting product function. It's done this way because
    $$
    \int_{0}^L \exp\left(\frac{2\pi}{L}(m-n)u\right) du \propto \delta_{mn}
    $$
     
  4. Mar 30, 2016 #3

    Ssnow

    User Avatar
    Gold Member

    Yes, the elements ##\{e^{jnx}\}## form an orthonormal system on your Hilbert space ...
     
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: Q about Fourier Coefficient Derivation
  1. Fourier Coefficients (Replies: 1)

Loading...