Matched Z Transformation

The matched z transformation uses the same pole-mapping Eq.(8.2) as in the impulse-invariant method, but the zeros are handled differently. Instead of only mapping the poles of the partial fraction expansion and letting the zeros fall where they may, the matched z transformation maps both the poles and zeros in the factored form of the transfer function [362, pp. 224-226].

The factored form [449] of a transfer function

can be written as

The matched z transformation is carried out by replacing each first-order term of the form by its digital equivalent , i.e.,

to get

Thus, the matched z transformation normally yields different digital zeros than the impulse-invariant method. The impulse-invariant method is generally considered superior to the matched z transformation [343].

---

Subsections

• Relation to Finite Difference Approximation

---

Previous: Impulse Invariant Method
Next: Relation to Finite Difference Approximation

Order a Hardcopy of Physical Audio Signal Processing

---

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.