Coupled Fractional Ambiguity Function

The ambiguity function is a vital analytical instrument for characterizing radar waveform attributes, such as time-delay and Doppler resolutions. This paper introduces the coupled fractional ambiguity function (CFrAF), a novel generalization that extends the utility of the classical ambiguity function. We present a theoretical framework for the CFrAF, deriving its fundamental properties such as time-frequency shifts, Moyal’s identity, and the inversion formula. As a consequence of Moyal’s identity, we also establish the maximum and volume properties of the proposed function.