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The compressive sensing (CS) theory says that for some kind of signals there is no need to keep or transfer all the data acquired accordingly to the Nyquist criterion. In this work we investigate if the CS approach is applicable for recording and analysis of radio astronomy (RA) signals. Since CS methods are applicable for the signals with sparse (and compressible) representations, the compressibility of RA signals is verified. As a result, we identify which RA signals can be processed using CS, find the parameters which can improve or degrade CS application to RA results, describe the optimum way how to perform signal filtering in CS applications. Also, a range of virtual LabVIEW instruments are created for the signal analysis with the CS theory.