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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 bedifferent 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.
An analog signal is a continuous function of a continuous variable. Referring to , this corresponds to that both the 1st AND the 2nd axis is continuous. The 1st axiswill in general correspond to the variable $t$ , meaning time. In this context we define
A time discrete signal is a continuous signal of a discrete variable. Referring to , we have the 1st axis discrete while the 2nd axis is continuous. Often we assign the values of the 1st axis to a variable $n$ . Time discrete signals often originate from analog signals being sampled.More on that in the Sampling theorem chapter.
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.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 samplinganalog signals and the samples being assigned to a discrete value.
All the signals mentioned above can be periodic. For time discrete and digital signals one has to be extra cautious when "declaring" periodicity as wewill see in Frequency definitions&periodicity . shows a periodic signal with period ${T}_{0}$ and an aperiodic signal.
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