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!

Integral Approximation

  1. Mar 21, 2013 #1

    If tau<<T which of the following relations are true:

    [tex]\int_{\tau/(1+a)}^{(T+\tau)/(1+a)}v(t)e^{-j2\pi f_0 at}e^{-j2\pi\frac{k}{T}t[1+a]}\,dt=\int_{0}^{T/(1+a)}v(t)e^{-j2\pi f_0 at}e^{-j2\pi\frac{k}{T}t[1+a]}\,dt[/tex]


    [tex]\int_{\tau/(1+a)}^{(T+\tau)/(1+a)}v(t)e^{-j2\pi f_0 at}e^{-j2\pi\frac{k}{T}t[1+a]}\,dt\simeq\int_{0}^{T/(1+a)}v(t)e^{-j2\pi f_0 at}e^{-j2\pi\frac{k}{T}t[1+a]}\,dt[/tex]

  2. jcsd
  3. Mar 23, 2013 #2
    Your assumtion is not enough to show one of the relations is true. It seems you need to show that the integrand is periodic with [itex] T/(1+\alpha)[/itex].
  4. Mar 23, 2013 #3
    OK, the integral after substituting for v(t) will look like:


    Is that enough to tell now?

  5. Mar 23, 2013 #4
    If that is the final version of the integral then it is enough to say that the equality holds.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook