In the present article we will discuss about all the discrete signals which are made up of discrete data or sampled data or also known as digital data of control system. Now before we discuss this topic in detail it is very important to know what is the need of digital technology even though we have analog system.
So let us examine first a few benefits of computerized framework over simple framework.
- Digital system has less power consumption as compared to analog system.
- Digital systems can easily handle non-linear systems which is the most important advantage of digital data in control systems.
- Because digital systems operate on logical operations, they exhibit decision-making properties that are very useful in today’s world of machines.
- They are more reliable than analog systems.
- Digital systems are readily available in compact sizes and are light in weight.
- They operate on instructions, we can program them to suit our needs, so we can make them more versatile than analog systems.
- Various complex tasks can be easily performed with high degree of accuracy with the help of digital technology.
Suppose you have a continuous signal, how do you convert this continuous signal to discrete signals? The answer to this question is very simple with the help of sampling process.
Sampling Process:
The process of sampling is defined as converting an analog signal into a digital signal with the help of a switch (also called a sampler). A sampler is a continuous on-off switch that converts analog signals directly into digital signals. We can have a series of sampler connections depending on what we use them for. For an ideal sample, the output pulse width is very small (tends to zero). Now when talking about discrete systems, it is very important to know about changes of z. We will discuss here the transformations of z and its utility in discrete systems. The Z-transform in discrete systems has the same role as the Fourier transform in continuous systems. We now discuss the transformation of z in detail.
We define the z transform as
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