Continuous and discrete signals

A message sent by means of an information carrier will be called a signal. In the general case, continuous and discrete signals are physical processes that change over time. Such processes may contain different characteristics. The one that is used to represent messages is called the signal parameter.

A message sent by means of an information carrier will be called a signal. In the general case, continuous and discrete signals are physical processes that change over time

Fig. 1. The procedure for sampling a continuous signal.

In the case where the signal parameter takes a finite number of values in a consistent time (all of which can be numbered), the signal is called discrete, and the message transmitted by such signals is a discrete message. The information transmitted by the source is also called discrete in this case. If the source produces a continuous message (respectively, the signal parameter is a continuous function of time), the corresponding information is called continuous. An example of a discrete message is the process of reading a book, the information in which is represented by text, i.e. a discrete sequence of individual icons (letters). An example of a continuous message is human speech transmitted by a modulated sound wave.

Continuous signals can be represented by a continuous function, for example, given on a certain interval [a, b] (see Figure 1). Continuous signals can be converted into discrete signals (this procedure is called sampling). To do this, from an infinite set of values of this function (signal parameter), select a certain number, which can approximately characterize the remaining values. One way to choose this is as follows. The domain of the function definition is divided by points x1, x2, ... xn, into segments of equal length and on each of these segments the value of the function is assumed to be constant and equal, for example, to the mean value on this segment; The function obtained at this stage is called stepped in mathematics. The next step is to project the "steps" values onto the axis of the function values (ordinate axis). The sequence of values of the function y1, y2, ... yn obtained in this way is a discrete representation of a continuous function, the accuracy of which can be infinitely improved by Reducing the lengths of segments of the partition of the range of values of the argument.

The axis of the values of the function can be divided into segments with a given step and display each of the selected segments from the domain of the function definition into the corresponding segment of the set of values (Figure 1). As a result, we obtain a finite set of numbers, determined, for example, in the middle or one of the boundaries of such segments.

Thus, any signal can be represented as a discrete, in other words, a sequence of signs of some alphabet.

The possibility of digitizing a continuous signal with any desired accuracy (to increase the accuracy it is enough to reduce the pitch) is fundamentally important from the point of view of computer science. A computer is a digital machine, that is, an internal representation of information in it is discrete. The sampling of the input signals (if it is continuous) makes it possible to make them suitable for computer processing.

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