Conditional monitoring for industrial IoT often uses acoustic signals for non-invasive anomaly detection. The acoustic sensors capture the mixed sound of several working machines, which should be separated in per-machine components for further analysis. The accuracy can be in part improved by installing redundant acoustic sensors. However, this would increase the amount of the transmitted data. In this paper, we propose a joint application of (i) Blind Source Separation (BSS) to separate the mixed sound of several working machines, and (ii) Compressed Sensing (CS) for reducing the amount of data transmitted over the network for partially correlated data sources. We also propose a set of key performance indicators to evaluate the whole system. Our simulation results, performed using the FastICA and CVXPY libraries, show that our solution provides a well balance between the amount of transmitted data and the separation quality. In other words, it optimizes the network throughput for the given value of desired separation quality.