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I have 3 signal sampled at 12 KHz frequency obtained from a motor rotating at constant 2000, 2020, and 2040 rpm. For 1 second signal recording I have 12,000 time samples. Depending on the frequency I can say (1/f) is the time period of oscillation.

But I am confused how to segment the signal with one time cycle from the whole signal, so that I can choose those many samples out of 12000 samples.

Is there any mathematical way to compute length of 1 cycle of signal when its sampling frequency and rpm are given, without observing the peak to peak in oscilloscope?

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Although it is hardly related to DSP but here is a quick calculation:

$R$ Rotations per minute is $\frac{R}{60}$ Rotations per second which gives $12K$ samples per second. Hence, One rotation is proportional to $\frac{1}{\frac{R}{60}}\times 12000 = \frac{720,000}{R}$ samples. For instance, for $2000$ RPM there are $360$ samples per rotation.

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