The analysis of multiple linear chirp singnals

This paper presents a technique for the analysis and extraction of multiple linear chirps in a time signal. These signals occur in nature and are becoming increasingly important in sonar, geophysical, ultrasonic and radar applications. The work is based on and closely related to the fractional Fourier transform (FrFT), which was introduced in its current form by Namias in 1979, although the principles underlying the FrFT can be found in the work of Wiener and Weyl in the 1920s. The paper considers discrete analysis and synthesis of complex signals containing linear chirps with various characteristics. We show how individual chirps in a mixture of chirps (not necessarily linear) can be extracted and investigate the filtering and reconstruction of mixed chirp signals. Examples are presented to illustrate the concepts using both synthetic signals and real data. A visual interpretation of the magnitude and phase of the analytic results is introduced allowing a range of transform orders to be viewed simultaneously. The filtering of linear and 'near-linear' chirp signals is also discussed alongside the efficient pulse compression characteristics of the FrFT.