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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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.