This paper considers the real-time recovery of a fast discrete signal (e.g., updated every T seconds) by using sparsely sampled sensor measurements whose sampling intervals are much larger than T (e.g., MT and NT, where M and N are integers). When the fast signal is an autoregressive moving average process, we propose an online information recovery algorithm that reconstructs the missing, fast time series by a complementary modulation of the sensor speeds MT and NT, and by a model-based fusion of the sparsely collected data. We provide the collaborative sensing design, parametric analysis, existence of solutions, and optimization of the algorithm. Application to a closed-loop disturbance rejection problem reveals the feasibility to reject fast disturbance signals fully with only slow sensors in real time, and in particular, the rejection of narrow-band disturbances whose frequencies are much higher than the Nyquist frequencies of the sensors.