Electrical – Is there something as common frequency

signalwave

Let's say I have following three sinusoidal waves.

 1. x1(t) = A*sin(2*pi*1000*t) i.e, f = 1 kHz   
 2. x2(t) = B*sin(2*pi*1500*t) i.e, f = 1.5 kHz   
 3. x3(t) = C*sin(2*pi*2000*t) i.e, f = 2 kHz

So when I get the signal y(t) = x1(t) + x2(t) + x3(t),

Is there any way to determine the common frequency such that the y(t) will start repeating itself? Can it be directly evaluated as smallest common multiple of these frequencies? For example, 6 kHz for this case.

Best Answer

The interval of repetition will be the LCM (least common multiple) of the periods of the sinusoids. This is also the inverse of the GCD (greatest common divisor) of the frequencies.

The periods of your signals are 1ms, 0.666ms, and 0.5ms. The LCM of these is 2ms, so the signal repeats after 2 periods of the first signal, 3 periods of the second signal, and 4 periods of the third signal.

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