National Instruments Order Analysis Toolset - page 43

Chapter 4 Resampling-Based Order Analysis
© National Instruments Corporation 4-3 LabVIEW Order Analysis Toolset User Manual
a larger margin of samples for analysis and need to resample 2.5K samples
in one revolution.
Most of the time, a tachometer does not produce enough pulses in one
revolution. Therefore, you need to multiply the number of pulses generated
by the tachometer, that is, interpolate the time sequence for a smaller angle
interval. When you interpolate the time sequence for a smaller angle
interval, you need a constant rate integer factor interpolation filter. The
LabVIEW Order Analysis Toolset uses a cascaded integrator-comb (CIC)
filter when interpolating the time sequence for a smaller angle. The transfer
function of the CIC filter is given by the following equation.
,
where L is the interpolation factor and n is the order.
The CIC filter has the advantage of only using a few samples in the original
time sequence to obtain a single, resampled point, while maintaining good
accuracy when the original signal is a narrow-band signal. Rotational speed
usually does not change very quickly in a couple of revolutions. Therefore,
the original time sequence is an exactly narrow-band signal and suitable for
interpolating with the CIC filter. You can implement the CIC filter using
only addition and subtraction operations, which makes the CIC filter very
efficient for online processing. Figure4-2 shows the power spectrum of the
original time sequence and the CIC interpolation filter with an interpolation
factor of eight.
Hz() 1
Ln
----- 1zL
–
1z–
-------------


n
=