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Generalizations of Cyclostationary Signal Processing: Spectral Analysis and Applications by Antonio Napolitano

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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 img and img replaced by x and y, respectively, for notation simplicity):

(7.346) equation

Accounting for the Fourier transform pairs

(7.347) equation

and (Champeney 1990, p. 81)

(7.348) equation

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) equation

where OA[·] denotes the Linear Canonical Transform (LCT) operator (Ozaktas et al. 2001) with parameter matrix

(7.350) equation

which is coincident with a Fresnel transform with λz = − γ.

In the case of finite-power stochastic ...

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