- #1
yoran
- 118
- 0
Hi,
I was wondering what substitution to try when finding a particular solution for a recurrence equation with a linear combination of impulses on the right side of the equation. I think an example will clarify this.
Given the recurrence equation
[tex]y[k+2]-4y[k]=\delta [k] + 2\delta [k+1][/tex]
with [tex]\delta [k][/tex] being the discrete impulse, i.e [tex]\delta [k] = 1[/tex] for [tex]k=0[/tex] and [tex]\delta [k] = 0[/tex] for [tex]k\neq 0[/tex].
First you must find a solution for the homogeneous equation. I have no problems with that. But I don't know what substitution to use for finding the particular solution? Can someone help me with that?
Thanks,
Yoran
I was wondering what substitution to try when finding a particular solution for a recurrence equation with a linear combination of impulses on the right side of the equation. I think an example will clarify this.
Given the recurrence equation
[tex]y[k+2]-4y[k]=\delta [k] + 2\delta [k+1][/tex]
with [tex]\delta [k][/tex] being the discrete impulse, i.e [tex]\delta [k] = 1[/tex] for [tex]k=0[/tex] and [tex]\delta [k] = 0[/tex] for [tex]k\neq 0[/tex].
First you must find a solution for the homogeneous equation. I have no problems with that. But I don't know what substitution to use for finding the particular solution? Can someone help me with that?
Thanks,
Yoran