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}}

     

  2. Time Scaling / Multiplication

  3. Time Reversal

  4. Differentiation

  5. Convolution

  6. Correlation

  7. Initial Value theorem

  8. Final Value theorem

    Problems on  ZT and ZT properties:

     

  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}}

     

  2. Time Scaling / Multiplication

  3. Time Reversal

  4. Differentiation

  5. Convolution

  6. Correlation

  7. Initial Value theorem

  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}}

     

  2. Time Scaling / Multiplication

  3. Time Reversal

  4. Differentiation

  5. Convolution

  6. Correlation

  7. Initial Value theorem

Final Value theorem

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