Exploiting Early Time Response Using the Half Fourier Transform (HFT)

Abstract

The singularity expansion method (SEM) proposed by Baum1 has been applied to quantify an electromagnetic response in an expansion of complex resonances of the system2.It has been shown that the dominant complex natural resonances of a system are a minimal set of parameters that define the overall physical properties of the system.3 So, a transient scattering response is analyzed in terms of the damped oscillations corresponding to the complex resonant frequency of the scatterer or target. In general, the signal model of the observed late time of an electromagnetic-energy-scattered response from an object can be written as

$$ y(t) = x(t) + n(t) \approx \sum\limits_{m = 1}^M {R_m \exp (s_m t) + n(t);0 \leqslant t \leqslant T,} $$

((1))

where y(t) is the observed time domain response, n(t) is the noise in the data, x(t) is the signal, R _m is the mth residue or complex amplitude, s _s = -α_m + jω_m, α_m is the mth damping factor, and ω_m is the mth angular frequencies (ω_m = 2πf_m).