Why not use a complex number in the exponent in the z-transform?

1. What is the limitation of Z-transform?
2. What is the condition for Z-transform to exist?
3. Why do we use Z-transform instead of Laplace transform?
4. What is the importance of the z transformation formula?

What is the limitation of Z-transform?

Limitations – The primary limitation of the Z-transform is that using Z-transform, the frequency domain response cannot be obtained and cannot be plotted.

What is the condition for Z-transform to exist?

For stability the ROC must contain the unit circle. If we need a causal system then the ROC must contain infinity and the system function will be a right-sided sequence. If we need an anticausal system then the ROC must contain the origin and the system function will be a left-sided sequence.

Why do we use Z-transform instead of Laplace transform?

The Z-transform is used to analyse the discrete-time LTI (also called LSI - Linear Shift Invariant) systems. The Laplace transform is used to analyse the continuous-time LTI systems. The ZT converts the time-domain difference equations into the algebraic equations in z-domain.

What is the importance of the z transformation formula?

The Z-Transform is an important tool in DSP that is fundamental to filter design and system analysis. It will help you understand the behavior and stability conditions of a system.