Although signals in the real world are always complex, they can be decomposed and then described compositionally, that is, as a function of the descriptions of their components. According to the Fourier theorem, all signals (under certain idealisations) can be decomposed into terms of component sinusoid signals, and operations and transformations on signals in general can therefore described as functions of operations and transformations on their component sinusoid signals.
In order to understand signal operations and transformations in detail, it is helpful to define a basic set of simple, idealised unit signals from which more complex signals can be built. Unit signals are signals whose amplitude and frequency are defined with respect to the value 1. Using the notion of unit signal, even a sinusoid can be regarded as being composed of simpler signals, for example as the sum of (potentially infinite) set of unit pulse signals. The unit pulse is one of the most useful idealised concepts available in signal processing, and facilitates the definition (and understanding) of filter systems.
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