Factored Form
By the fundamental theorem of algebra, every th order polynomial
can be factored into a product of
first-order polynomials.
Therefore, Eq.
(6.5) above can be written in
factored form as
The numerator roots
![$ \{q_1,\ldots,q_M\}$](http://www.dsprelated.com/josimages_new/filters/img674.png)
![$ \{p_1, \ldots,
p_N\}$](http://www.dsprelated.com/josimages_new/filters/img675.png)
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Z Transform of Difference Equations