A Performance Analysis System for the Sport of Bowling

• The angular velocity graph is highly sensitive to a "phase shift" that can occur in
the waveform when the ball crosses under the pin deck light. Referring back to
Figures 2-2a and 2-2b in Section II, the pin deck light is bright enough that it can
alter the duration of the last revolution significantly, depending on the orientation
of the light sensor as the ball approaches the pins. Consequently, the revolution
location algorithm detects a longer (or shorter) duration than actually occurred,
artificially inflating or deflating the final angular velocity of the ball. Figure 3-10
illustrates this phenomenon.
Light Level
140
120
100
80
60
Last complete
Revolution
Phase
Shift
Impact
(Head Pin)
40
20
0
2000
2100 2200 2300 2400 2500 2600 2700 2800
Milliseconds (since Release)
Figure 3-10: Pin Deck Phase Shift, Impact Region (800 ms)
Figures 3-11a and 3-11b indicate the adverse effects of this "phase shift" on the
analysis of the waveform. The analysis captured in Figure 3-11a was performed
on the waveform with the phase-shifted portion of the raw data included. The
angular velocity begins to roll off 10 feet in front of the pins. The same
waveform was used for the analysis captured in Figure 3-11b, but the phaseshifted
portion of the raw data was excluded from the calculations. As a
consequence, Figure 3-11b shows the angular velocity continuing to increase all
the way through impact with the pins.
The difference in the two raw data waveforms is only 50 msec (6 sample times),
but the difference in the resulting analysis is dramatic. The simplest method for
correcting the problem is to find the pin impact point in the waveform, and then
exclude from the spectrum calculation the 50-75 msecs (6-9 samples) that
immediately precede pin impact. After the raw data waveform has been filtered,
the time is reinserted by extrapolating the results of the angular velocity extraction
routine back into the excluded data.
The problem arises because the filtered waveform that is used for all of the
analysis calculations is reconstructed for time-independent frequency content.
Using an FFT function over the entire waveform at one time yields frequency
components of the data, but does not reveal when those frequencies were present
in the waveform. A more advanced technique would be to use wavelet methods
in the spectrum calculations to yield time-correlated frequency content.
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