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!

Homework Help: Sum of sinosoids that can be a Fourier Series expansion

  1. Aug 26, 2016 #1
    1. The problem statement, all variables and given/known data
    I was given a problem with a list of sums of sinusoidal signals, such as
    Example that I made up: x(t)=cos(t)+5sin(5*t). The problem asks if a given expression could be a Fourier expansion.
    2. Relevant equations

    3. The attempt at a solution
    My guess is that it has something to do with 5 being an integer multiple of 1.
  2. jcsd
  3. Aug 26, 2016 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Can you write your sum as$$
    \cos t + 5\sin(5t) = a_0 + \sum_{n=1}^\infty \left ( a_n\cos(\frac {n\pi t} p) + b_n\sin(\frac {n\pi t} p)\right )$$
    by choosing certain values for the ##a_n,~b_n,~p##? Hint: lots of them can be ##0##.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted