The purpose of this post is to provide detailed explanation about Aliasing phenomena and how it will reflect in the measured signal.

Aliasing – Facts:

“Aliasing creates erroneous signal due to insufficient sampling”.

As per Nyquist Criteria, The sample rate must be greater than or equal to two times the highest frequency component in the input signal (i.e. Fs = 2*Fmax). If this rule is violated, unwanted or undesirable signals appear in the frequency band of interest. This is called “Aliasing”.

We could never see Aliasing in the modern vibration analyzers as they are all equipped with Anti-Aliasing filters.

Example:

Consideration:

Sampling Frequency = 16 Hz

Total no of samples = 16

That means, the maximum frequency that could be viewed properly is 8 Hz.

As per Nyquist rule, if there is any frequency component above 8 Hz (Fs/2) present in the signal, it must create erroneous signal (the signal which is not really present in the input) in the frequency band of Interest. Let’s have a step by step look with different input signals for the above sampling criteria. The amplitude of the signal is taken as 2 units.

Here, Sampling time = Total no of samples / Sampling Frequency = 1 Second

Input Signal Frequency = 1 Hz / Sampling Frequency = 16 Hz / Total no of samples = 16

Input Signal Frequency = 2 Hz / Sampling Frequency = 16 Hz / Total no of samples = 16

Input Signal Frequency = 3 Hz / Sampling Frequency = 16 Hz / Total no of samples = 16

Input Signal Frequency = 4 Hz / Sampling Frequency = 16 Hz / Total no of samples = 16

Input Signal Frequency = 5 Hz / Sampling Frequency = 16 Hz / Total no of samples = 16

Input Signal Frequency = 6 Hz / Sampling Frequency = 16 Hz / Total no of samples = 16

Input Signal Frequency = 7 Hz / Sampling Frequency = 16 Hz / Total no of samples = 16

Input Signal Frequency = 7.9 Hz / Sampling Frequency = 16 Hz / Total no of samples = 16

Input Signal Frequency = 9 Hz / Sampling Frequency = 16 Hz / Total no of samples = 16

Input Signal Frequency = 10 Hz / Sampling Frequency = 16 Hz / Total no of samples = 16

Input Signal Frequency = 11 Hz / Sampling Frequency = 16 Hz / Total no of samples = 16

Input Signal Frequency = 12 Hz / Sampling Frequency = 16 Hz / Total no of samples = 16

Input Signal Frequency = 13 Hz / Sampling Frequency = 16 Hz / Total no of samples = 16

Input Signal Frequency = 14 Hz / Sampling Frequency = 16 Hz / Total no of samples = 16

Input Signal Frequency = 15 Hz / Sampling Frequency = 16 Hz / Total no of samples = 16

The frequency of the signal is correctly measured till the input signal is 7.9 Hz (Little less than half the sampling rate). When the input signal has any frequency component higher than 8 Hz, The frequency of the signal measured at the output would be “Sampling frequency – Input frequency”. The phenomena of generating erroneous signal is called as Aliasing.

Additionally, It could be noted that, when the number of samples per vibration cycle is lesser than ten, the signal is not really sampled as a proper sinusoidal wave. There are sampling noises in the measured signal (3 Hz to 7.9 Hz), whereas the 1 Hz signal and to some extent, the 2 Hz signal, are sampled as a sinusoidal wave. The sampling noise caused due to this insufficient sampling, though it satisfies Nyquist criteria, is called Eyeball sampling.

Reference:

Advanced Vibration Analysis by Nelson Baxter, J.L. Frarey, and R. Kelm