# Z -Transform Properties

Updated on 2017/07/28 19:16

Write introduction of the Article here.

1. ### Linearity

Statement:

If  $x_{1}(n)+x_{2}(n) \leftrightarrow X_{1}(z)+X_{2}(z)$ then $a x_{1}(n)+ b x_{2}(n) \leftrightarrow a X_{1}(z)+ b X_{2}(z)$, where a & b are any arbitrary constants.

Proof:

ZT of the sequence x(n) is given as:

$X(z)=\sum_{n=-\infty }^{ \infty } x(n) z^{^{-n}}$

1. ### Linearity

Statement:

If  $x_{1}(n)+x_{2}(n) \leftrightarrow X_{1}(z)+X_{2}(z)$ then $a x_{1}(n)+ b x_{2}(n) \leftrightarrow a X_{1}(z)+ b X_{2}(z)$, where a & b are any arbitrary constants.

Proof:

ZT of the sequence x(n) is given as:

$X(z)=\sum_{n=-\infty }^{ \infty } x(n) z^{^{-n}}$

1. ### Linearity

Statement:

If  $x_{1}(n)+x_{2}(n) \leftrightarrow X_{1}(z)+X_{2}(z)$ then $a x_{1}(n)+ b x_{2}(n) \leftrightarrow a X_{1}(z)+ b X_{2}(z)$, where a & b are any arbitrary constants.

Proof:

ZT of the sequence x(n) is given as:

$X(z)=\sum_{n=-\infty }^{ \infty } x(n) z^{^{-n}}$

### Problems on  ZT and ZT properties:

 $\delta (n)$ u(n) $\delta (n-2)$ u(n-2) $\delta (n+2)$ u(n+2) u(-n-1)

$\delta (n)$ :          $\delta (n) \leftrightarrow 1$

### Problems on  ZT and ZT properties:

 $\delta (n)$ u(n) $\delta (n-2)$ u(n-2) $\delta (n+2)$ u(n+2) u(-n-1)

$\delta (n)$ :          $\delta (n) \leftrightarrow 1$

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Created by PRIYANKA BHOSALE on 2017/07/27 17:21

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