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Important Properties of Z-Transform & Applications

Learn key properties of z-transform in digital signal processing, including linearity, time shifting, convolution, and more. Understand how to apply these properties effectively.

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Important Properties of Z-Transform & Applications

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  1. Digital signal processing Done By: IssraaJwadKazim Lec. 8

  2. PROPERTIES OF THE Z TRANSFORM Some of the important properties of the z transform are stated below : 1) Linearity property:

  3. 2) Time shifting property :

  4. 3) Multiplication by an exponential (an) : 4) Multiplication by a ramp (Differentiation in the z-domain) : 5) Time reversal property:

  5. 6)Convolution in Time domain:

  6. The z-transform of the above sequence has already been found as • X(z) = z/z-a, with ROC : |z|>|a| . • 3) x(n) = -bn u(-n-1) • The z-transform of the above sequence has been found as ; • X(z) = z/z-b, with ROC : |z| <|b| .

  7. 4) x(n) = u(n) (Unit step sequence):

  8. ie., X(z) = z / (z-1) , with |z| < 1 which defines the ROC of the z transform. • The ROC in this case, is the interior of a circle of radius ‘1. 6) Unit ramp sequence : x(n) = n u(n) We use differentiation property of z transform to solve this problem: The property states that

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