difference equation for discrete time

Discussion in 'Homework Help' started by hamza324, Nov 23, 2011.

  1. hamza324

    Thread Starter Member

    Jul 10, 2011
    33
    1
    i got following question and i am trying to find out the initial conditions

     y[n+2] +ay[n+1]+by[n]= 0  \ \ for\ n>=0

    where  a=\frac{-5}{6} and b={1}{6}

    this is what i solved for initial conditions;

     for n=-2 \ \ \Rightarrow \ \ y[0]=0

     for n=-1 \ \ \Rightarrow \ \ y[1]=0

    Are these correct initial conditions?
     
  2. t_n_k

    AAC Fanatic!

    Mar 6, 2009
    5,448
    782
    I would imagine you assign the initial conditions as whatever you wish to them to be - within reason.

    Since the function is, by definition, valid only for n>=0 you cannot then evaluate the value of variable y for n=-2 or -1. You are therefore obliged to assign values for y(0) and y(1) from which you could calculate a sensible value of y(2) at the initial 'iteration'.

    Assigning y(0)=0 and y(1)=0 may not be helpful since

    y(2)=(5/6)*y(1)-16*y(0)=0

    And at the next and subsequent iterations the latest value of y will always be zero.

    So obviously it would be of little use assigning y(0)=0 and y(1)=0.
     
Loading...