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

Euler theorem in Prony method

  1. Oct 17, 2011 #1
    I read in various articles about Prony analysis that

    [itex]{\displaystyle \sum_{i=1}^{L}}A_{i}e^{\sigma_{i}t}cos(2\pi f_{i}t+\phi_{i})[/itex]

    Using Euler theorem this equals:

    [itex]{\displaystyle \sum_{i=1}^{L}}A_{i}e^{\sigma_{i}t}\left(\frac{e^{j2\pi f_{i}t}e^{j\phi_{i}}}{2}+\frac{e^{-j2\pi f_{i}t}e^{-j\phi_{i}}}{2}\right)[/itex]

    [itex]={\displaystyle \sum_{i=1}^{L}}\left(\frac{A_{i}e^{(j2\pi f_{i}+\sigma_{i})t}e^{j\phi_{i}}}{2}+\frac{A_{i}e^{(-j2\pi f_{i}+\sigma_{i})t}e^{-j\phi_{i}}}{2}\right)[/itex]

    is supposed to be equal to

    {\displaystyle \sum_{i=1}^{N}}\frac{A_{i}}{2}e^{j\phi_{i}}e^{(σ_{i}+j2\pi f_{i})t}

  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted

Similar Discussions: Euler theorem in Prony method
  1. Euler's method error (Replies: 1)