Relation to Finite Difference Approximation

The Finite Difference Approximation (FDA) (§7.3.1) is a special case of the matched transformation applied to the point . To see this, simply set in Eq.(8.5) to obtain

which is the FDA definition in the frequency domain given in Eq.(7.3).

Since the FDA equals the match z transformation for the point , it maps analog dc () to digital dc () exactly. However, that is the only point on the frequency axis that is perfectly mapped, as shown in Fig.7.15.

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About the Author: 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.