What is signal ?

The most fundamental function in electrical communications is the sinusoidal signal because,
1. The response of a sine wave to a linear time invariant system is also sinusoidal, i.e, if a sinusoidal signal is applied at the input of a linear system. The output waveform is also sinusoidal with the same frequency as the input, except for a constant transmission delay and gain (or attenuation)
2. The sinusoidal analysis of electrical networks is even more simple and convenient.
(The terms signal and function are interchangeably used as there is no difference between the two A function is defined as a set of rules which substitute one number for another. A "signal is a function of time and therefore, "signal" may be defined as a set of rules to assign a number f(t) for every number t, a time domain.
However, communication systems involve waveforms that are complex in nature, and it is desirable to resolve them in terms sinusoidal functions. Signal analysis is a tool for achieving this aim. signal analysis may be defined as the method of resolving a function in terms of an infinite series. The method suggested by J.B.J.Fourier for signal analysis povides the original of the theory of Fourier series and Fourier transform,