Relationship between z-transform and DFT

1. What is the relationship between Z-transform and DFT?
2. How does Z-transform contribute to the analysis of DT systems?
3. Why we use Z-transform for discrete time signal?
4. What is the relationship between DTFT and DFT?

What is the relationship between Z-transform and DFT?

Also, if r = 1, then the discrete time Fourier transform (DTFT) is same as the Z-transform. In other words, the DTFT is nothing but the Z-transform evaluated along the unit circle centred at the origin of the z-plane.

How does Z-transform contribute to the analysis of DT systems?

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.

Why we use Z-transform for discrete time signal?

The other advantage of the z-transform is that it allows us to bring in the power of complex variable theory to bear on the problems of discrete time signals and systems. Given an analog signal x(t), it could be represented as discrete time signal by a sequence of weighted & delayed impulses.

What is the relationship between DTFT and DFT?

The DTFT itself is a continuous function of frequency, but discrete samples of it can be readily calculated via the discrete Fourier transform (DFT) (see § Sampling the DTFT), which is by far the most common method of modern Fourier analysis. Both transforms are invertible.