Z Transform is a very useful mathematical tool, mainly used to solve difference equations. It converts the difference equations into algebraic form, which are then easy to be solved and then the solution is inversely converted, using Inverse Z Transform, to the form it should initially be. It is the discrete equivalent of the Laplace Transform and a generalization of the Discrete Time Fourier Transform.
Example 1: Causal Finite Duration Sequence
Example 2: Delta Function δ(n)
Example 3: Unit Step Function u(n)
Example 6: Differentiation in Z
Example 5: Transformation of Equation
Partial Fraction Expansion Method
The Inverse Z Transform allows us to recover the discrete time sequence from the Z function:
Example 1: Solving Difference Equation
Example 2: Solving Difference Equation
Difference Equations with Unilateral Z Transform
Example 3: Solving Difference Equation with Initial Conditions
Example 4: Solving Difference Equation with Initial Conditions
Difference equations are called the equations of which the present value of the discrete output is function of the present and previous values of the discrete input and the previous values of the discrete output. For example a difference equation is:
