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\section{Introduction}  If you Fourier transform a quasi-sinusoidal signal with a quadratic phase evolution then the Fourier transform can be approximated using the Fresnel integrals. However, what if your signal has a cubic phase evolution? Can you go beyond the Fresnel integrals? This is to expand on the work of \cite{GSDThesis} \citet{GSDThesis}.  In this particular case we are interested in signal that may have intrinsic cubic phase evolution, but the majority of any cubic component is from Doppler shifting of the signal e.g.\ in a binary system orbit.