Home | Introduction to Z Transform

For analysis of continuous time LTI system Laplace transform is used. And for analysis of discrete time LTI system z transform is used. Z

**PREREQISTING DISCUSSION ABOUT Z
TRANSFORM**

For
analysis of continuous time LTI system Laplace transform is used. And for
analysis of discrete time LTI system z transform is used. Z transform is
mathematical tool used for conversion of time domain into frequency domain (z
domain) and is a function of the complex valued variable Z. The z transform of
a discrete time signal x(n) denoted by X(z) and given as

Z
transform is an infinite power series because summation index varies from -∞ to ∞. But it is useful for values of
z for which sum is finite. The values of z for which f (z) is finite and lie
within the region called as ―region of convergence (ROC).

**ADVANTAGES OF Z TRANSFORM**

1. The DFT
can be determined by evaluating z transform.

2. Z
transform is widely used for analysis and synthesis of digital filter.

3. Z
transform is used for linear filtering. z transform is also used for finding
Linear convolution, cross-correlation and auto-correlations of sequences.

4. In z transform user can characterize LTI
system (stable/unstable, causal/anti- causal)
and its response to various signals by placements of pole and zero plot.

**ADVANTAGES OF ROC(REGION OF CONVERGENCE)**

1. ROC is
going to decide whether system is stable or unstable.

2. ROC
decides the type of sequences causal or anti-causal.

3. ROC also
decides finite or infinite duration sequences.

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