Chapter: Digital Signal Processing - Signals and System

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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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