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Module by: Anders Gjendemsjø. E-mail the author

Summary: Introduction to the Signals chapter

To describe signals and to understand that signals can carry information we need tools for mathematical description and manipulation of signals.

In this chapter we introduce several important signals and show simple methods of describing them. Depending on which type of signals we are looking at, it will be different methods availiable for manipulating them. The elementary operations for manipulating signals and sequences will be described.

The simplest signals are one-dimensional and what follows is a classification of them.

Classification of signals

Analog signals

An analog signal is a continuous function of a continuous variable. Referring to Figure 1, this corresponds to that both the 1st AND the 2nd axis is continuous. The 1st axis will in general correspond to the variable tt, meaning time. In this context we define

  • signal range - the possible amplitude values the signal can take
  • signal axis - the time interval for which the signal exists
Figure 1: Reference axes
Figure 1 (axes.png)

Time discrete signals

A time discrete signal is a continuous signal of a discrete variable. Referring to Figure 1, we have the 1st axis discrete while the 2nd axis is continuous. Often we assign the values of the 1st axis to a variable nn. Time discrete signals often originate from analog signals being sampled. More on that in the Sampling theorem chapter.

Figure 2: Time discrete signal
Figure 2 (time_discrete.png)
Note that the signal is only defined for integer values along the 1st axis. We do not have any information other than the values at index points.

Digital signals

Let the signal be a discrete function of a discrete variable, e.g. 1st and 2nd axis discrete, then the signal will be digital. Examples of digital signals are a binary sequence. Digital signals often arise from sampling analog signals and the samples being assigned to a discrete value.

Periodic vs non periodic signals

All the signals mentioned above can be periodic. For time discrete and digital signals one has to be extra cautious when "declaring" periodicity as we will see in Frequency definitions & periodicity. Figure 3 shows a periodic signal with period T0T0 and an aperiodic signal.

Figure 3: (Figures by Melissa Selik)
(a) Periodic signal
Figure 3(a) (sigclass3.png)
(b) Aperiodic signal
Figure 3(b) (sigclass4.png)

Matlab file

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