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!

Trying to understand difference equation

  1. Jul 9, 2013 #1

    I hope someone can help me with a problem I am having. It is neither homework or coursework, but for my own understanding.

    I should say from the start, I am one of those people who tend not to be able to see the forset because all the trees are in the way, so I probably will be missing something very obvious to others.

    At the minute, I am trying to get better at dealing with difference equations when it comes to designing digital filters. The book I have been reading through gives the following difference equation

    h(n) = b1 . h(n - 1) + δ(n)

    With the following table for the results

    n δ(n) h(n - 1) h(n)
    0 1
    1 0
    2 0
    3 0
    4 0

    Here, h(n) is the response, and δ(n) is the impulse function.

    I hope someone can help me see how the rest of the table is formed. When I understand the process I will be able to apply it better to other problems.

  2. jcsd
  3. Jul 9, 2013 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    Your recursion only makes sense for n = 0 if you have access to h(-1) to start things off; that is, you need an "initial condition" such as h(-1)=c; then, for all n >= 0, the recursion determines all the other h(n) values. Just plug things into the recursion: h(0) = b_1 *c + δ(0), h(1) = b_1*h(0) + δ(1), etc. That's all there is to it!

    A more difficult (and more interesting) question would be: find a closed-form formula for h(n) in terms of the initial condition h(-1) = c, the constant b_1 and the given form of {δ(k), k >=0}.
  4. Jul 13, 2013 #3


    User Avatar
    Homework Helper

    δ(n) is a function such that
    δ(n)=0 when n is not 0

    δ(n)=δ(n) h(n - 1) h(n)
    since h(- 1) h(0)=1
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted