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The use of frames is analyzed in Compressed Sensing (CS) through proofs and experiments. First, a new generalized Dictionary-Restricted Isometry Property (D-RIP) sparsity bound constant for CS is established. Second, experiments with a tight frame to analyze sparsity and reconstruction quality using several signal and image types are shown. The constant k δ is used in fulfilling the definition of D-RIP. It is proved that k-sparse signals can be reconstructed if 2 2 3 k δ < by using a concisedoi:10.4236/jsip.2016.71006 fatcat:v56oelyaqbbqxiugktfwgfdwb4