Effects of Pre-Processing on the ECG Signal Sparsity and Compression Quality

Pre-processing is necessary for many applications before data transmission. In this paper, signal sparsity variations due to some pre-processing steps such as filtering and compression are considered; and after complete and educational reviewing preliminaries, it is shown that (i) Adding noise to a signal decreases the signal sparsity and increases the diversity index named Gini-Sympson as a special case of Tsallis entropy; (ii) the sparsity of filtered signal is increased; (iii) the compression metrics such as PRD and CR are improved if the compressed sensing method is performed on the filtered signal; and finally (iv) it is tried that the theoretical explanations are validated numerically.