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!

Uniform linear splines is my equation correct?

  1. Nov 4, 2012 #1
    The question as stated: Define the uniform linear splines Hk:=H0(x−k), k=−1,0,1,2,3, where

    H0={x, 0≤x<1,

    2−x, 1≤x<2,

    0, otherwise.

    For k=−1, I would get:

    H−1={x+1, 1≤x<2,

    1−x, 2≤x<3,

    0, otherwise.

    Is that correct?

    Thank you.
     
    Last edited: Nov 4, 2012
  2. jcsd
  3. Nov 4, 2012 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    No. ##H_{-1}## would be ##H_0## translated one unit to the left. You moved it to the right.
     
  4. Nov 4, 2012 #3

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    H−1(x)=H0(x+1), right?
    H0(x)={x+1, 0≤x<1,
    2−x, 1≤x<2,
    0, otherwise}​
    To get H0(x+1), wouldn't you write x+1 for x everywhere in the definition of H0(x)?
     
  5. Nov 4, 2012 #4
    LCKurtz-Wouldn't I just plug in k=-1, into H_0(x-(-1))=H_0(x+1)?
     
  6. Nov 4, 2012 #5
    haruspex-

    I accidently put x+1 for the first function in H0, it's supposed to be x.

    Yes, I see what you mean. I thought I did that though:
    H−1={x+1, 1≤x<2,

    1−x, 2≤x<3,

    0, otherwise.

    I don't see what I'm doing wrong...
     
  7. Nov 4, 2012 #6

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    No, you should have got:
    H0(x+1)={x+1, 0≤x+1<1,
    1−x, 1≤x+1<2,​
     
  8. Nov 4, 2012 #7
    Oh okay, I see what you mean. I though I could evaluate it at the inequalities. Thanks!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook