Exploiting early time response using the fractional Fourier transform for analyzing transient radar returns

This paper presents a new technique for estimating parameters of damped sinusoids and impulse-like responses utilizing both early and late time transient scattering responses. Transient scattering responses are composed of damped sinusoids at late times and impulse-like components at early times. Due to the impulse-like components, it is difficult to extract meaningful damped sinusoids when analyzing the complete data set. In this paper, the entire time-domain response is used to extract the signal parameters of interest utilizing both the early and late times. The fractional Fourier transform (FrFT), especially the half Fourier transform (HFT), is used to analyze the data for parameter identification. Impulse or Gaussian-like pulses can be easily separated from the late time damped exponentials in the HFT domain, as they have similar functional representations. In addition, the damped exponentials have a turn on time which needs to be solved for. Results from two examples show that the new technique is applicable for signals that are composed of damped exponentials with a turn-on time and short pulse-like components.