**1.Linearity Property:-**

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we know that Bi-lateral Z- Transform of a signal is .

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**2.Time-shifting Property:-**

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we know that .

. Let

Here n is a variable and k is a constant.

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from the above equation forms Z Transform pair with .

**3. Scaling in-Z-domain property:-**

we know that .

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**4. Time-reversal property:-**

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we know that .

. Let ,

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from the above equation forms Z Transform pair with .

**5****. Differentiation in Z-domain:-**

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we know that .

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from the above equation forms Z-Transform pair with and the ROC is same as that of the original sequence x[n].

**6. Convolution in Time-domain:-**

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we know that .

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