PREREQISTING DISCUSSION ABOUT Z
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
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.
transform is widely used for analysis and synthesis of digital filter.
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.
decides the type of sequences causal or anti-causal.
3. ROC also
decides finite or infinite duration sequences.