# difference equation for discrete time

#### hamza324

Joined Jul 10, 2011
33
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?

#### t_n_k

Joined Mar 6, 2009
5,455
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.