Discrete signals - Z Transforms

1. What is the z-transform of the discrete-time signal?
2. Is z-transform only for discrete signals?
3. Why is Z transformation needed in discrete systems?
4. How are discrete-time systems analyzed using Z transforms?

What is the z-transform of the discrete-time signal?

Explanation: The z-transform of a real discrete time sequence x(n) is defined as a power of 'z' which is equal to X(z)=\sum_n=-\infty^\infty x(n)z^-n, where 'z' is a complex variable.

Is z-transform only for discrete signals?

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.

Why is Z transformation needed in discrete systems?

z transforms are particularly useful to analyze the signal discretized in time. Hence, we are given a sequence of numbers in the time domain. z transform takes these sequences to the frequency domain (or the z domain), where we can check for their stability, frequency response, etc.

How are discrete-time systems analyzed using Z transforms?

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.