Electronic applications
Electronic applications

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3.2 Characteristics of discrete-time and continuous-time signals

A continuous-time signal is shown in Figure 15(a). The signal is continuous because it has a value at any instance of time – that is, for any value of t, it is possible read a value of x of t from the graph. Most signals in the real world are continuous in time. For example, if you were monitoring the temperature of a room, you would be able to take a measured value of temperature at any time.

Described image
Figure 15 (a) Continuous-time signal; (b) discrete-time signal

A discrete-time signal (sometimes referred to as a time-discrete signal or simply a discrete signal) is shown in Figure 15(b). In the rest of this course the standard convention of drawing the vertical lines in a discrete-time signal with a round dot on the end will be used; these lines-with-dots are often called ‘lollipops’. The signal in Figure 15(b) is discrete because it only has a value at fixed points placed at discrete time intervals cap t seconds apart along the x-axis. cap t is called the sampling interval. Values of x of n can be found for the integer values of n, such as n equals one, n equals two, etc., but there is no value for the signal at, say, n equals 1.5. Thus n represents the number of the sample.

It is hard to think of examples of real-world discrete-time signals, since most real-world signals are continuous; however, if you took the temperature reading of a room every day at the same time, the result would be a discrete-time signal. Most discrete-time signals come from sampling continuous-time signals to get them into a digitised form that can be processed by digital computers.

Activity 6

Timing: Allow about 5 minutes

State whether the following are discrete-time signals or continuous-time signals, giving a reason for each answer:

  • a.the wind speed across the blades of a wind turbine
  • b.the position of a robotic arm as it picks items from a conveyor belt
  • c.the total distance travelled by the robotic arm each hour over a 24-hour period.

Answer

  • a.The wind speed is a continuous-time signal, because you can take a reading at any time.
  • b.The robotic arm always has a position – even if it is in a resting position, you know where it is – so this is a continuous-time signal.
  • c.The total distance travelled by the robotic arm is recorded just once in each hour, so this is a discrete-time signal. Over a 24-hour period there will be 24 discrete values recorded.

In the next section you will learn how a continuous signal is converted to a discrete signal.

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