## 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

 (7.6)

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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Z Transform of Difference Equations