Resampling

When applying an FFT to even-time-spaced samples, or a time waveform, you can calculate the frequency components that are periodic in time. Order components, however, take place n times per revolution and are periodic in rotational angle. Signals that are evenly-spaced in rotation angle are even-angle signals. You can think of even-angle signals as those acquired when a machine rotates over a constant angle. If sound or vibration samples are evenly-spaced in rotation angle, you can apply an FFT to the even-angle-spaced samples to calculate the order components that are periodic in rotational angle. You can use standard FFT methods to perform order analysis with an even-angle signal.

In order to acquire even-angle samples, you must adjust the sampling rate of your DAQ device according to the rotational speed. The adjusted sampling rate is a synchronous sampling rate. In practice, you need complex additional hardware to set a variable sampling rate to acquire samples with a synchronous sampling rate. Applying anti-alias filtering also is difficult when the sampling rate is variable. Thus, when you acquire a sound and vibration signal with a fixed sampling rate you should then use software to resample the signal with a synchronous sampling rate.

The following figure shows the effect of resampling on a simulated vibration signal in a run-up test.

Each point on the two shafts represents a sampling position. The left-hand shaft illustrates even-time-spaced sampling. As the shaft rotates faster, the intervals between adjacent samples become greater. Accordingly, the period of the signal gets smaller, and the frequency span becomes wider. With so many elements changing, identifying the characteristic components is difficult. After resampling, however, all the samples appear with constant angle intervals, as you can see from the right-hand shaft. The period of the even-angle signal is constant, and you then can identify the order components.