7.8 Spectral Analysis of Doppler-Stretched Signals –Constant Relative Radial Acceleration
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
(7.347) 
and (Champeney 1990, p. 81)
(7.348) 
with a = πγ, we have that the Fourier transform of a delayed, frequency shifted, and chirp modulated signal (7.346) can be expressed as
(7.349) 
where OA[·] denotes the Linear Canonical Transform (LCT) operator (Ozaktas et al. 2001) with parameter matrix
(7.350) 
which is coincident with a Fresnel transform with λz = − γ.
In the case of finite-power stochastic ...
Get Generalizations of Cyclostationary Signal Processing: Spectral Analysis and Applications now with the O’Reilly learning platform.
O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.
