1. Not finding help here? Sign up for a free 30min 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!

Difference Equations

  1. Sep 4, 2006 #1
    Folks,

    I'm a bit rusty on difference eqns. Here's the problem:

    [tex] y_n -0.5 y_{n-1} = x_n [/tex]

    Here's what I can get out of it so far:

    [tex] y_1 -0.5 y_0 = x_1 [/tex]
    [tex] y_2 -0.5 y_1 = x_2 [/tex]
    [tex] y_3 -0.5 y_2 = x_3 [/tex]

    I just need some sense of direction, not a solution. It seems to me that this kind of problem requires that some boundary conditions be given, but that is not the case. That's all I have! Maybe it's something very simple I can't see right now.

    Any help is highly appreciated.
     
  2. jcsd
  3. Sep 4, 2006 #2

    rbj

    User Avatar

    so you have a difference equation. what are you trying to do with it?

    are you trying to figure out what [itex]y_n[/itex] is? do you know what [itex]x_n[/itex] is?
     
  4. Sep 4, 2006 #3
    I assume the goal is to get [tex]y_n[/tex] since that was not explicitly stated. The directions are simply "solve the difference equation". That doesn't help much, does it? I do not have [tex]x_n[/tex]
     
  5. Sep 4, 2006 #4

    0rthodontist

    User Avatar
    Science Advisor

    It's already about as solved as it can get if you don't know the x's.
     
  6. Sep 4, 2006 #5
    Yes, but the answer wouldn't be that obviuous; it sounds like there is information missing, as rbj pointed out. I'll go talk to my instructor. As soon as I find out the answer or have another question, I'll get back to you guys. Thanks for all the help!
     
  7. Sep 4, 2006 #6
    Have you been learning about z-transforms?

    y[n] -> Y(z)
    y[n-1] -> Y(z)/z

    then solve for Y(z) = f(X(z)), then transform back to y[n] = f(x[n]) and you will have eliminated the y[n-1].
     
  8. Sep 5, 2006 #7
    Z-transforms really work on this kind of problem. I've found a book with a very easy-to-follow introduction. Thanks for the hint. Here is my answer:

    [tex]h[n] = -2^{-n}u[n-1][/tex]
     
  9. Sep 5, 2006 #8
    One thing to be careful about with z-transforms is that some functions, such as [tex] H(z) = \frac{1}{1-az^{-1}}[/tex], have multiple inverse transforms. Which to use depends on the region of convergence of H(z), which affects (or is defined by) the stability and causality of the system.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Difference Equations
  1. Difference equation (Replies: 5)

  2. Difference equation (Replies: 4)

  3. Difference Equation (Replies: 1)

  4. Difference equations (Replies: 5)

  5. Difference Equations (Replies: 5)

Loading...