State and prove the Z-transform properties x_1[n] circledstar x_2[n] leftrightarrow ^z X_1(z) X_2(z) ROC_x1 intersection ROC_x2, where R_x1 and R_x2 are the ROC_s of X_1(z) and X_2(z)respectively. nx[n] leftrightarrow ^z -z dX(z)/dz show that the ROC does not change.
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