Electronic – Why the resultant period of two signals is the LCM of the individual period of that signal?

frequencysignalsignal processingsignal-theory

Suppose a signal is constructed using two independent signals(say S1 and S2)both S1 and S2 have two different individual frequencies.The resultant signal that has been constructed has a new frequency,which is the LCM of the two frequencies of the signals S1 and S2 .Logically how can we justify and explain the above method.
Also there is a video tutorial on YouTube where I have seen this.Refer to it for any reference.
Here is the Video– 1. Understanding Fourier Series, Theory + Derivation.

He added a low frequency with a high frequency–enter image description here

Best Answer

This is just basic math.

It may be easier to think of this by considering the period rather than the frequency. If you have a signal with 1 second period and add to it a signal with ½ second period, for example, with what period will the combined signal repeat. The answer is obviously 1 second. Another way to look at this is that the ½ second signal is a harmonic of the 1 second signal. Adding harmonics doesn't change the fundamental frequency.

For the harmonic addition logic to be valid, added signals have to actually be harmonics. That means their frequencies must be integer multiples of the fundamental. Therefore, the problem is finding the fundamental of a set of frequencies. The fundamental is the highest frequency that all the others are integer multiples of. What you are looking for is therefore the largest common denominator. Note that this largest common denominator of the frequency results in the same answer as the least common multiple of the period, which is what you seem to be asking about.