Factor into sum of terms

fletch

Can anyone help...I need the following factored into a sum of terms

fletch

anybody....?

Son Goku

Is that a function of a complex variable or a real variable?
I'm presuming the former.

fletch

Son Goku wrote:

Is that a function of a complex variable or a real variable?
I'm presuming the former.

Not a 100% either way....I've included the whole question below. All I know is that I need the denominator as a sum of terms so that I can apply partial fractions to it. Thanks for your help

Michael Collins

Ah yes inverse Z transforms are quite tricky at first but their grand once you get a feel for them. Just remember that Z^-1 is bacially the delay operator. For example, if you have a sequence like so: h(n)=...0, 0, 0, 1, 5, -3, 2, 0, 0,...
Now the sequence isn't completly defined yet as we don't know where it starts. Let the 0 index start at the first "1" so we have:

h(0)=1
h(1)=5
h(2)=-3
h(3)=2
h(4)=0
h(n>4)=0
and also h(n<0)=0

So the Z transform of this sequence is then H(Z)=1+5*(Z^-1)-3*(Z^-2)+2*(Z^-3). So we can see if we get any Z transform into this form it'll be very easy to solve.

You have Z^-2/(1-0.9*Z^-1). The way I'd solve this would be to perform long division of the denominator into the numberator like so:

___________
1-0.9*Z^-1 | Z^-2               

So dividing this we get the quotient as: Z^-2+0.9*Z^-3+(0.9)^2*Z^-4+...etc. We can easily get the Inverse Transform of this as per above...Probably best you finish it off yourself, you learn more that way (and I've a big lunch waiting for me ).

Let me know if you want me to clarify anything above...