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I think its name derives from the fact that the signal waves provided by this instrument, are function (of the time) signals. E.g. sine function, triangle (linear function), square (constant function).
https://en.wikipedia.org/wiki/Function_generator
mathematically every signal can be taken as a function of the variable of our choice.
in this case the variable is time.
The So called function generator generates electrical signals which are some funtions of time.
so it is called so.
In my standpoint this is so because it would prevent confusing it with the name "generators". Another reason, to my mind, is that it can provide not only the sine function, but also various other functions, including ramp, pulse, and etc.
function generator differs from an oscillator in that it generates different wave forms that does not include a special feedback circuit, while oscillator is a signal generator through an amplifier in feedback mechanisim
the signal generated by this instrument, are the function of the time. In general every signal can be taken as a function of the variable of our choice
The basic functions by which a system is analyzed are the sinuoid, triangular and square waveforms. These can be generated using the function generator.
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