Results 1 to 1 of 1

Thread: Exponential averaging with 2 time constants

  1. #1
    Newbie
    Joined
    May 2012
    From
    Under the sun
    Posts
    1

    Exponential averaging with 2 time constants

    Hello,

    let $\displaystyle f(t) = \sin^2(a \cdot t)$ with $\displaystyle a > 0$ some constant.

    How do I calculate $\displaystyle x(t) = \int_{-\infty}^{t} f(t') e^{-\frac{t-t'}{\tau(t')}} \text{d}t'$ where $\displaystyle \tau(t) = \begin{cases} \tau_0, & f(t) \ge x(t)\\ \tau_1, & \text{else} \end{cases}$ with $\displaystyle \tau_0 \ge 0$ and $\displaystyle \tau_1 \ge 0$ constant? I am particularly interested in $\displaystyle \lim_{t \to \infty} \{ \max x(t) \}$ and in the respective minimum.

    In words, we are exponentially averaging a function $\displaystyle f(t)$ with different smoothing constants for increasing and decreasing function values relative to the smoothing result. E.g., whenever $\displaystyle f(t_0) \ge x(t_0)$ for some $\displaystyle t_0$, the function is considered rising and the smoothing constant $\displaystyle \tau(t_0) = \tau_0$ is used.

    Thank you for any hint.
    Last edited by Golan; May 31st 2012 at 12:22 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. how to find time in exponential equation.
    Posted in the Algebra Forum
    Replies: 4
    Last Post: Nov 22nd 2011, 12:56 PM
  2. Voltage drops and time constants in d.c. circuit???
    Posted in the Math Topics Forum
    Replies: 0
    Last Post: Sep 3rd 2011, 05:03 AM
  3. Replies: 5
    Last Post: Jul 13th 2010, 02:11 PM
  4. 2 server exponential queue time
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: Dec 12th 2008, 07:49 AM
  5. Exponential expected service time question
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: Nov 4th 2008, 02:03 AM

Search Tags


/mathhelpforum @mathhelpforum