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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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University