In the case of constant relative radial acceleration, under the narrow-band conditions (7.246a) and (7.246b), the complex received signal is given by the chirp modulated signal (7.240) (with and replaced by x and y, respectively, for notation simplicity):
Accounting for the Fourier transform pairs
and (Champeney 1990, p. 81)
with a = πγ, we have that the Fourier transform of a delayed, frequency shifted, and chirp modulated signal (7.346) can be expressed as
where OA[·] denotes the Linear Canonical Transform (LCT) operator (Ozaktas et al. 2001) with parameter matrix
which is coincident with a Fresnel transform with λz = − γ.
In the case of finite-power stochastic ...