It is important that there is no information in the sampled waveform near the sampling frequency to avoid a problem called aliasing.
Here the actual signal is represented in black and the sampled representation of it is in gray. The vertical lines represent the sampling frequency. Note that if the sampling frequency is the same as the sampled frequency, each sample is the same size, and the output of the sampling circuit will be a constant direct voltage -- obviously having no relation to frequency of the input signal.
Now note what happens if the actual signal is higher in frequency than the sampling frequency. The sampler output looks like a very low frequency, and again it is not a correct representation of the actual signal. This phenomenon is called aliasing, and it can lead to gross errors unless it is avoided. The best way to avoid aliasing is to pass the input signal through an analog low-pass filter whose cut-off frequency is less than one-half the sampling frequency. In most modern FFT analyzers, the sampling frequency is set to 2.56 times the filter cut-off frequency. The filter must have a very sharp cut off characteristic, or roll off, and this means it will also have Phase Shift that can affect the data if one needs phase information near the upper end of the frequency span of the analyzer. To avoid this, select a frequency span so the frequency in question is in the lower half of the frequency range. This is important in performing balancing with an FFT analyzer, where phase of the 1X vibration signal is needed.
Aliasing also occurs in other media, such as motion pictures. For instance, sometimes in western movies the wagon wheel spokes may appear stopped, or rotating backward. This is optical aliasing, for a movie is a sampled representation of the original motion. Another example of optical aliasing is the stroboscope, which is set to flash at a rate equal to or near the rotation rate of the object being observed, making it appear stationary or slowly turning.
Sampling Rules for Digital Signal Analysis
The data path must contain an analog Anti-Aliasing low-pass filter
You must sample at least twice as fast as the highest frequency to be analyzed
The Frequency Response of the analysis depends on the sampling frequency
These rules apply to all FFT analysis, and the analyzer automatically takes care of them. The anti-aliasing filter is internally set to the appropriate value for each frequency range of the analyzer. The total sampling time is called the time record length and the nature of the FFT dictates that the spacing between the frequency components in the spectrum (also called the frequency resolution) is 1 divided by the record length. For instance, if the frequency resolution is one Hz, then the record length is one second, and if the resolution is 0.1 Hz, then the record length is 10 seconds, etc. From this it can be seen that in order to perform high resolution spectrum analysis relatively long times are required to collect the data. This has nothing to do with the speed of the calculations in the analyzer; it is simply a natural law of frequency analysis.
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