Chirp signal transform and its properties

Abstract

The chirp signal exp (i π (x - y)2) is a typical example of CAZAC (constant amplitude zero autocorrelation) sequence. Using the chirp signals, the chirp z transform and the chirp-Fourier transform were defined in order to calculate the discrete Fourier transform. We define a transform directly from the chirp signals for an even or odd number N and the continuous version. We study the fundamental properties of the transform and how it can be applied to recursion problems and differential equations. Furthermore, when N is not prime and N = M L, we define a transform skipped L and develop the theory for it.