# Nyquist Criterion

While taking a vibration signature in FFT mode (Fast Fourier Transform) we must decide on the sampling rate. This is the rate at which we collect data for proper digital transform to a desired FFT. If the rate is either too fast or too slow we would not get the right signature.

The problem starts since all vibration signals we collect through our sensors (like accelerometer) are analog in nature and to get a useful discrete time signal (from which an FFT is made) we must sample often enough.

But too many samples would be expensive and possibly redundant unless we use the samples to draw a continuous graph. If we take too less then we would miss out on important information and make a wrong understanding of the signal.

So, what we are looking for?

What we are actually looking for is the ratio between the sampling period and the true oscillation period that is just right or ‘critical’.

Then the question is how many samples should we take in each up and down oscillation of a sinusoid?

It turns out that this critical sampling period or called the Nyquist criterion has two samples per oscillation.

So to take a proper FFT, our sampling rate must be twice the maximum frequency we would be interested in. For example, if the maximum frequency that we might be interested to capture is say 200 Hz (or 200 oscillations per second) then our sampling rate must be 400 samples per second.

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