The Z-Transform is the discrete time counter part of Laplace transform. Z-transform allows us to perform transform analysis of unstable systems and to develop additional insights and tools for LTI (linear Time Invariant)system analysis. The Z-transform transforms difference equation into algebraic equations and hence the discrete time system analysis is specified. Z Transform Basics with Z transform formulas are explained below,

The Z-Transform of a discrete time signal x(n) is defined as:

Where ‘z’ is a complex variable and z=r*e^ (j*ω)

Where ‘r’ is the radius of the circle.

If the sequence x(n) exists for ‘n’ in the range( -∞ to ∞), then,

If the sequence x(n) exists only for n>=0,then

The Z-Transform of a discrete time signal x(n) is defined as:

Where ‘z’ is a complex variable and z=r*e^ (j*ω)

Where ‘r’ is the radius of the circle.

If the sequence x(n) exists for ‘n’ in the range( -∞ to ∞), then,

represents a bilateral or two sided Z transform.

If the sequence x(n) exists only for n>=0,then

which is called one sided or unilateral Z-Transform.

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Z Transform