Application of z-transform

The z-transform is useful for the manipulation of discrete data sequences and has acquired a new significance in the formulation and analysis of discrete-time systems. It is used extensively today in the areas of applied mathematics, digital signal processing, control theory, population science, economics.

1. What are the advantages of z-transform?
2. How is z-transform used in the analysis of digital filters?
3. What kind of systems can be analyzed using z-transform?

What are the advantages of z-transform?

The z-transform is an important signal-processing tool for analyzing the interaction between signals and systems. A significant advantage of the z-transform over the discrete-time Fourier transform is that the z-transform exists for many signals that do not have a discrete-time Fourier transform.

How is z-transform used in the analysis of digital filters?

Just as analog filters are designed using the Laplace transform, recursive digital filters are developed with a parallel technique called the z-transform. The overall strategy of these two transforms is the same: probe the impulse response with sinusoids and exponentials to find the system's poles and zeros.

What kind of systems can be analyzed using z-transform?

In the same way, the z-transforms changes difference equations into algebraic equations, thereby simplifying the analysis of discrete-time systems. The z-transform method of analysis of discrete-time systems parallels the Laplace transform method of analysis of continuous-time systems, with some minor differences.