Figure 4-3. hs(t) with fs = 1, Slow roll compensation, Slow roll compensation -5 – National Instruments Order Analysis Toolset User Manual
Page 45
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(nT
s
) with the following equation.
(4-1)
where h
s
is a sinc function defined by
.
Figure 4-3 shows the plot of h
s
(t) with f
s
= 1.
Figure 4-3. h
s
(t) with
f
s
= 1
You can resample the signal at the equal angle interval time instance by
evaluating Equation 4-1 at the desired time. Before resampling, 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
new sampling 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
of the resampled signal improves.
Slow Roll Compensation
In 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.
xˆ t
( )
x nT
s
(
)h
s
nT
s
t
–
(
)
n
∑
=
h
s
t
( )
sinc f
s
t
( )
π f
s
t
(
)
sin
π f
s
t
----------------------
=
=