Connexions module: m10422 1
Chirp-Z Transform
∗
phil schniter
This work is produced by The Connexions Project and licensed under the
Creative Commons Attribution License
†
Abstract
This module covers the fundamentals of Chirp Z-Transform.
1 Chirp-Z Transform
Note: There are other ways to sample circles, segments, or spirals in z-domain that have fast (FFT-like)
transforms.
(a) (b) (c)
Figure 1
Perhaps the most famous is the CZT
X(zl) =
N−1
X
n=0
x[n]AV −ln∀l, l ={0, . . . , N −1}
(1)
A=A0eiθ0
is the starting point.
V=V0eiφ0
spirals in if
V0>1
,
spirals out if
V0<1
,
and circles if
V0= 1
.
∗
Version 2.9: May 31, 2009 6:10 pm GMT-5
†
http://creativecommons.org/licenses/by/1.0
http://cnx.org/content/m10422/2.9/