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# Properties of Z Transform (ZT)

1) Linearity 2) Time shifting 3) Scaling in z domain 4) Time reversal Property 5) Differentiation in z domain 6) Convolution Theorem 7) Correlation Property 8) Initial value Theorem 9) Final value Theorem

PROPERTIES OF Z TRANSFORM (ZT)

1) Linearity

The linearity property states that if z

z Transform of linear     combination of two or more signals is equal to the same linear combination of z transform of individual signals.

2) Time shifting

The Time shifting property states that if z x(n)

Thus shifting the sequence circularly by „k  samples is equivalent to multiplying its z transform by z –k

3) Scaling in z domain

This property states that if

Thus scaling in z transform is equivalent to multiplying by an in time domain.

4) Time reversal Property

The Time reversal property states that if z

It means that if the sequence is folded it is equivalent to replacing z by z-1 in z domain.

5) Differentiation in z domain

The Differentiation property states that if z

6) Convolution Theorem

The Circular property states that if z

Convolution of two sequences in time domain corresponds to multiplication of its Z transform sequence in frequency domain.

7) Correlation Property

The Correlation of two sequences states that if z

8) Initial value Theorem

Initial value theorem states that if z

9) Final value Theorem

Final value theorem states that if z

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