  We define the accumulated spectrogram associated to a locally trace class
orthogonal projection operator and to a bounded set using the polar
decomposition of its restriction on that set and prove a convergence theorem
for accumulated spectrograms along an exhaustion in the case when the
corresponding determinantal point process is hyperuniform. We prove that a
radial determinantal point process on Rd is always hyperuniform along the
exhaustion formed by the dilations of a bounded open set, and as a consequence,
we obtain that dilations of the corresponding accumulated spectrogram converge
to the indicator function of the considered set, establishing thus a universal
phenomenon. Our result is a generalisation of a theorem by
Abreu-Gr\"ochenig-Romero in [1] concerning time-frequency localization
operators.
