The analysis of signals containing multiple chirps

Abstract

The analysis of signals containing multiple chirps occurs in many situations in acoustics, for example, in the bioacoustics field in analyzing the sounds of bats and dolphins. In sonar and seismic, chirp signals are used because of their pulse compression properties. Recently, the fractional Fourier transform has shown that linear chirp signals may be recognized and this has greatly facilitated the use of these signals. This paper shows a method similar to that of the fractional transform and shows how other types of chirp signals, polynomial, and other functional forms may also be analyzed. It also looks at the resolution that can be achieved when separating chirps both in rate and in time. This is of particular relevance when dealing with dispersion in the propagation of signals through different media. Examples will be presented, for the analysis of some bat signals and for some seismic signals. The analysis of signals in the time frequency domain using piecewise linear chirps will also be demonstrated, and some further examples from synthetic seismic signals will be demonstrated.