Abstract
This study generalises the definition of ambiguity function (AF) by deriving the generalised definition based on the signals in the fractional Fourier domain, and also proves the property that the coordinate-rotated AF by an angle is equivalent to the AF of the signals after being fractional Fourier transformed with that angle. Combined with the modified algorithm for projecting generalised AF on coordinate axes, an analytic expression for Radon-ambiguity transform directly based on signals, instead of the AF, is deduced in this study. For sampled signals, the proposed algorithm for Radon-ambiguity transform can be realised by using the fast Fourier transform, and is computationally efficient. At the end of this study, simulation results validate the rotational property of AFs and also demonstrate the performance of the algorithm.
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