Chirp Signal Transform and Its Properties

Abstract

The chirp signal $\mathrm{\text{exp}}(i\pi (x-y{)}^2)$ 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 $N=ML$, we define a transform skipped $L$ and develop the theory for it.