On the Fractional Wideband and Narrowband Ambiguity Function in Radar and Sonar

We construct the wideband ambiguity function for signals represented by their fractional Fourier transforms. Because the reflected signal must be represented as a Doppler scaled version of the transmitted signal, this wideband form of ambiguity does not enjoy many of the same properties as the narrowband form (which is formed from a Doppler shifted version of the signal). We present the general result and also examine an approximation appropriate to wideband signals reflected from slowly moving targets