We introduce the concept of determinantal point processes (DPPs) associated with locally trace-class self-adjoint operators and also the notion of hyperuniformity of point processes. For a given bounded set and a locally trace class operators, one can define the accumulated spectrogram, which is closely related to the density of points in the DPP. The spectrogram is defined through the short-time Fourier transform which is often used in the time-frequency analysis. We then present a convergence theorem for accumulated spectrograms along an exhaustion formed by dilations of a bounded set, which can be viewed as a version of the well-known circular law observed in the Ginibre point process. This talk is based on a joint work with Pierre Lazag and Makoto Katori.