The Chirp z-Transform Algorithm and Its Application

In dealing with sampled data the z-transform plays the role which is played by the Laplace transform in continuous time systems. One example of its application is spectrum analysis. The computation of sampled ^-transforms, which has been greatly facilitated by the fast Fourier transform algorithm, is further facilitated by the "chirp z-transform" algorithm described in this paper.1-2 * Mr. Rader is with Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, Massachusetts. Lincoln Laboratory is operated with support from" the U. S. Air Force. 1249 1250 TI-IE BELL SYSTEM T E C H N I C A L J O U R N A L , M A Y - J U N E 19G9 The 2-transform of a sequence of numbers xn is defined as X(z) = £ xnz~n, 71---- C O (1)