A data storage device is disclosed comprising a head actuated over a disk, and a sensor configured to generate a sensor signal representing at least one of a shock and a thermal popping affecting the data storage device. The sensor signal is first filtered based on a first frequency range corresponding to the shock to generate a shock signal, and second filtered based on a second frequency range corresponding to the thermal popping to generate a pop signal, wherein the second frequency range is different from the first frequency range. The shock signal and the pop signal are individually processed, for example, to log a disturbance event, to abort a write operation, or to generate a feed-forward servo compensation signal.