what is the general proof to the theorem in signals. i.e -"for any signal - discrete or continuous.. the condition for it to be periodic requires it to have a rational frequency"..?
a particular case of this proof could be arrived by assuming sinusoidal curve.
but that isn't general..
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Using the assumption of a linear circuit superposition applies. All signals can be expressed in a Fourier's Series therefore if it applies to one it applies to all. For none linear circuits as large base-emitter signal of a common emitter BJT circuit you must use another analysis.
Actually the proof of this comes from sinusoidal signals itself. Any PERIODIC signal can be expressed as a sum of sine and cosine terms terms right? Yes, there are other condition(Drcihlet's conditions), but lets not go into that. So, if its true for one sinusoid, it must be true for other sinusoid since each one has a frequency which is an integer multiple of the harmonics frequency. So its must be true for that periodic signal since its a sum of all those periodic signals. So it is true for any periodic signal.