The document discusses the Chirp Z algorithm, which is a generalization of the discrete Fourier transform (DFT). The Chirp Z transform samples points along spiral arcs in the z-plane rather than uniformly along the unit circle like the DFT. The algorithm calculates the Z transform at a finite number of points along a logarithmic spiral contour. It involves defining a new sequence and expressing the transform as a convolution to obtain the chirp z equation. Applications of the chirp z transform include processing chirp signals in radar, speech processing, and MRI data.

1. CHIRP Z ALGORITHM

2. CONTENTS
1.Introduction
2.Algorithm
3.Application

3. INTRODUCTION
•The chirp z-transform (CZT) is A generalization of the discrete fourier
transform (DFT).
•Dft samples the z plane at uniformly-spaced points along the unit circle,
the chirp z-transform samples along spiral arcs in the z-plane,
corresponding to straight lines in the s plane.

4. • Three special cases of CZT
1.Dft
2.Real DFT
3.Zoom DFT
• Chirp Z transform calculates the Z transform at A finite number of points zk along
A logarithmic spiral contour
A -complex starting point
W -complex ratio between points
M -number of points to calculate

5. Algorithm:-
1. For example, if the contour is A circle O F radius R and the Z* are N equally
spaced points, then
2.Suppose that the points Z* in the z-plane fall on an arc which begins at some point

6. 3. It spiral either toward origin or away from origin
……III
4. When points {z*k}in III are substituted into the expression for the Z transform,
we obtain
…..IV

7. Some example of contours

8. 5.By definition
……..V
6. We can express (IV) in the form o f a convolution, by noting that
………..Vi
7.By putting VI into IV we get,
……Vii
8. Let us define a new sequence g ( n) as
………Viii

9. 9.So,(vii)will be given as,
…….Ix
10.Equation IX gives us the chirp z equation.

10. Application
1.Chirp signal is used in radar.
2.Speech processing
3.For processing on MRI data.