  Phase coherence of charge carriers leads to electron-wave interference in
ballistic mesoscopic conductors. In graphene, such Fabry-P\'erot-like
interference has been observed, but a detailed analysis has been complicated by
the two-dimensional nature of conduction, which allows for complex interference
patterns. In this work, we have achieved high-quality Fabry-P\'erot
interference in a suspended graphene device, both in conductance and in shot
noise, and analyzed their structure using Fourier transform techniques. The
Fourier analysis reveals two sets of overlapping, coexisting interferences,
with the ratios of the diamonds being equal to the width to length ratio of the
device. We attribute these sets to a unique coexistence of longitudinal and
transverse resonances, with the longitudinal resonances originating from the
bunching of modes with low transverse momentum. Furthermore, our results give
insight into the renormalization of the Fermi velocity in suspended graphene
samples, caused by unscreened many-body interactions.
