Condition monitoring and predictive maintenance of industrial machinery require to continuously measure vibrations or wave data with a high sampling rate for accurate diagnosis. However, such measuring strategies cause high time and energy consumption for transferring and handling a large amount of data. For this reason, a compression sensing approach is investigated. Compression sensing is a technique that allows to completely reconstruct a signal from its samples, while sampling it below the Nyquist limit. It relies on the hypothesis of sparsity of the signal in some domain. In particular, the higher the sparsity level, the lower will be the dimension of the compressed measurements required to recover the original high-dimensional signal.