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Chirp-Z Transform

Module by: Phil Schniter

Summary: This module covers the fundamentals of Chirp Z-Transform.

Chirp-Z Transform

Note: There are other ways to sample circles, segments, or spirals in z-domain that have fast (FFT-like) transforms.

Figure 1
Subfigure 1.1Subfigure 1.2Subfigure 1.3
Subfigure 1.1 (spiral.png)Subfigure 1.2 (circle.png)Subfigure 1.3 (segment.png)

Perhaps the most famous is the CZT

X z l =∑n=0N-1xnAV-ln ∀l,l=0…N-1 X z l n 0 N 1 x n A V l n l l 0 … N 1 (1)

A= A 0 ⅇⅈ θ 0 A A 0 θ 0 is the starting point.

V= V 0 ⅇⅈ φ 0 V V 0 φ 0 spirals in if V 0 >1 V 0 1 ,

spirals out if V 0 <1 V 0 1 ,

and circles if V 0 =1 V 0 1 .

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