Chapter 4 Resampling-Based Order Analysis
© National Instruments Corporation 4-5 LabVIEW Order Analysis Toolset User Manual
According to the Nyquist sampling theorem, you can exactly reconstruct
the time signal x(t) from samples x(nTs) with the following equation.
(4-1)
where hs is a sinc function defined by .
Figure 4-3 shows the plot of hs(t) with fs = 1.
Figure 4-3. hs(t) with fs = 1
You can resample the signal at the equal angle interval time instance by
evaluating Equation4-1 at the desired time. Before resamplin g, you might
need a lowpass anti-aliasing filter if the new sampling rate is lower that the
previous sampling rate.
The LabVIEW Order Analysis Toolset uses a digital adaptive-interpolation
filter to complete the entire resample process. The bandwidth of the
adaptive-interpolation filter automatically changes according to the
newsampling rate to prevent the aliasing phenomenon. The stopband
attenuation of the interpolation filter controls the accuracy of the
resampling. As the stopband attenuation becomes higher, the accuracy
oft he resampled signal improves.
Slow Roll CompensationIn machine condition monitoring applications, engineers often use a
proximity probe to measure the movement of a shaft. The proximity probe
can convert the distance between the probe and the shaft into an electrical
signal.
x
ˆt() xnT
s
()hsnTst–()
n
∑
=
hst() sinc fst() πfst()sin
πfst
----------------------==