## 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 are called the

*zeros*of the transfer function, and the denominator roots are called the

*poles*of the filter. Poles and zeros are discussed further in Chapter 8.

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Series and Parallel Transfer Functions

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Z Transform of Difference Equations