## 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