A Performance Analysis System for the Sport of Bowling

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$Course Syllabus - Penn State Harrisburg Math/Computer Sciences ...$

$A Simulator for the MARIE Architecture - Penn State Harrisburg Math ...$

3.2 FILTERING THE RAW DATA Figure 3-4 is a capture of the "Spectrum" screen from the MASTER program, and demonstrates the use of digital signal processing (DSP) and, more specifically, the application of the Fast Fourier Transform (FFT) to the raw data waveform shown in Figure 3-1. By obtaining the frequency spectrum of the raw data, it is possible to identify and retain the fundamental frequencies, while removing the harmonic content and other noise. Applying the inverse FFT function (FFT -1 ) to the modified spectrum then yields the filtered waveform of Figure 3-5, which closely resembles the ideal waveform that was previously described [7,10]. Figure 3-4: MASTER "Spectrum" Screen Capture The MASTER program must be able to perform this filtering automatically, without any user input. Therefore, a reliable method for the MASTER to identify the fundamental frequency, and the band of frequencies of interest, must be developed. For this application, the fundamental frequency will be considered the component of the spectrum with the greatest magnitude in excess of 2.0 Hz. Looking at the spectrum of Figure 3-4, it is easy to identify the fundamental frequencies centered at ~7.5 Hz (disregarding the low-frequency components located below 2.0 Hz), with the first harmonic centered at twice the fundamental (~15 Hz). The magnitude of 44
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. 45
Page 1 and 2: The Pennsylvania State University T
Page 3 and 4: TABLE OF CONTENTS Section I: Introd
Page 5 and 6: LIST OF FIGURES Figure 2-1 SMARTDOT
Page 7 and 8: SECTION I: INTRODUCTION, BACKGROUND
Page 9 and 10: eceiver that stores, processes, and
Page 11 and 12: 1.3.2 Product Development Phase The
Page 13 and 14: SECTION II: COLLECTING THE DATA - T
Page 15 and 16: 2.2 Design Constraints The feasibil
Page 17 and 18: 2.3 SENSING REQUIREMENTS The module
Page 19 and 20: Pin Deck Light Foul Line Figure 2-2
Page 21 and 22: 2.4.1 Ambient Light Sensor The ambi
Page 23 and 24: 9 28 8 RST V CC V CC 5 6 hyst 7 3 +
Page 25 and 26: 2.6 HARDWARE/SOFTWARE INTERACTION D
Page 27 and 28: 2.6.3 Baud Rate The module communic
Page 29 and 30: Configuration settings and the samp
Page 31 and 32: 2.7.5 The Ball is Rolling If the wa
Page 33 and 34: covered by the wand). When the modu
Page 35 and 36: 2.8.1 Detecting Release Detecting t
Page 37 and 38: Light Level 100 90 80 70 60 50 40 3
Page 39 and 40: By filtering the data, and then cou
Page 41 and 42: The 'F300x can write to any portion
Page 43 and 44: One possibility is to use a transfo
Page 45 and 46: 2.10 SUMMARY This portion of the re
Page 47 and 48: The ball's angular velocity increas
Page 49: Light Level 100 90 80 70 60 50 40 3
Page 53 and 54: Since the fundamental frequency and
Page 55 and 56: Figure 3-7: MASTER "Analysis" Scree
Page 57 and 58: known, the linear momentum (and thu
Page 59 and 60: In order to find the value for v 1
Page 61 and 62: 3.5 ASSUMPTIONS AND ERROR ANALYSIS
Page 63 and 64: 3.5.3 External Forces and Friction
Page 65 and 66: 3.6.1 Implementation and Performanc
Page 67 and 68: Figure 3-11a: Effects of Phase Shif
Page 69 and 70: 3.6.3 The "Perfect" Game to Analyze
Page 71 and 72: Since the change in angular velocit
Page 73 and 74: BIBLIOGRAPHY [1] United State Paten
Page 75 and 76: APPENDIX A - SMARTDOT MODULE EMBEDD
Page 77 and 78: Appendix A: SMARTDOT Module Embedde
Page 85 and 86: APPENDIX B - SMARTDOT MODULE SOURCE
Page 87 and 88: Appendix C: SMARTDOT Module Command
Page 89 and 90: Figure C-3 Appendix C: SMARTDOT Mod
Page 91 and 92: APPENDIX E - 300 GAME MASTER SCREEN
Page 93 and 94: Appendix E: 300 Game Analysis Frame
Page 95 and 96: Appendix E: 300 Game Analysis Frame
Page 97: Appendix E: 300 Game Analysis Frame

A Performance Analysis System for the Sport of Bowling

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