A Performance Analysis System for the Sport of Bowling

the fundamental frequency has been normalized to 1.00, with the remainder of the
frequency components normalized relative to the fundamental frequency [7].
Extracting the desired waveform requires a bandpass filter that removes the unwanted
low and high frequencies while leaving the frequencies of interest unaltered. It is
important to note that the fundamental frequency will vary from bowler to bowler.
Consequently, a bandpass filter with fixed upper and lower bounds is not appropriate.
Instead, the MASTER must calculate the pass band dynamically for each bowler, and
possibly for each individual shot.
Several basic methods are appropriate for calculating the pass band limits. These limits
can be set based on:
• A percentage of the fundamental frequency.
• A percentage of the magnitude of the fundamental frequency.
• A combination of the first two.
There are two separate limits imposed on the upper band of the filter. First, the pass band
should not be allowed to extend into the harmonic portion of the spectrum, as this will
introduce components of the noise the filter is intended to remove. Second, the ball
reaches its highest angular velocity at the point of roll out, or at impact with the pins if it
doesn't roll out, and it can revolve, at most, 26.7 times in 60 feet (if it did not skid at all).
Combining that information with the time of transit of the ball, it is possible to apply an
upper bound to the maximum angular velocity of the ball and, therefore, the high side of
the bandpass filter.
The dashed orange line around the fundamental frequencies in Figure 3-4 represents the
adaptive bandpass filter for this spectrum. The MASTER program calculated these limits
automatically, using the third method listed above (through a combination of frequency
percentages and magnitudes). The MASTER identifies the fundamental frequency, and
then extends the pass band limits on either side of the fundamental until it finds an area of
"insignificant contribution". In this case, it finds a contiguous group of frequency
components with magnitudes less than 0.1 (10% of the fundamental).
The bandpass filter limits must also conform to minimum and maximum percentages of
the fundamental frequency. The spectrum shown is typical for the author's bowling style
and he has found that the minimum low cut-off frequency can be set relatively close to
the fundamental frequency (75% of the fundamental), while the high cut-off frequency
should be at least 125% of the fundamental, but no more than 175% of the fundamental.
Of course, these limits may differ for other bowlers.
With the pass band limits identified, a digital bandpass filter can now be applied to the
spectrum. The magnitudes of the frequency components within the pass band are
retained, while those outside the pass band are set to zero (0.00). Applying the inverse
FFT function (FFT -1 ) to the altered spectrum yields the waveform shown in Figure 3-5.
This filtered sinusoidal waveform describes the rotation of the finger hole that contained
the SMARTDOT module and, since the entire surface of the ball rotates at the same rate
as the finger hole, this waveform also describes the rotation of the ball. The 'C' source
code from the MASTER application for the adaptive bandpass filter implementation has
been included in Appendix D.
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