Vargas et al v. Pfizer Inc. et al

Filing 146

DECLARATION of Julie A. Ahrens in Support re: 141 MOTION for Attorney Fees and Costs.. Document filed by Brian Transeau. (Attachments: # 1 Exhibit A# 2 Exhibit B# 3 Exhibit C# 4 Exhibit D# 5 Exhibit E# 6 Exhibit F# 7 Exhibit G# 8 Exhibit H# 9 Exhibit H part 2# 10 Exhibit I# 11 Exhibit J# 12 Exhibit K# 13 Exhibit L# 14 Exhibit M# 15 Exhibit N# 16 Exhibit O# 17 Exhibit P# 18 Exhibit Q# 19 Exhibit R# 20 Exhibit S# 21 Exhibit T# 22 Exhibit U# 23 Exhibit V# 24 Exhibit W# 25 Exhibit X# 26 Exhibit Y# 27 Exhibit Z# 28 Exhibit Z part 2# 29 Exhibit AA# 30 Exhibit BB# 31 Exhibit CC# 32 Exhibit DD# 33 Exhibit EE# 34 Exhibit FF)(Falzone, Anthony)

Vargas et al v. Pfizer Inc. et al

Doc. 146 Att. 20

EXHIBIT S

Dockets.Justia.com

Berklee college of music
1140 Boylston Street, Boston, MA 02215-3693 Tel [phone] www.berklee.edu

Dr. Richard Boulanger
Professor, Music Synthesis Department [e-mail]

Brian Transeau (BT)
Binary Acoustics www.binaryacoustics.com

c/o Eric M. Stahl
Davis Wright Tremaine LLP 1501 4th Avenue Suite 2600 Seatle, WA 98101-1688 Voice: 206-628-7762 Fax: [phone]

[e-mail]

January 31, 2006
Regarding: "Vargas v. Pfizer, Inc. et al., SDNY Cause No. 04-CV-9772 (WHP) - Expert opinion and FFT Analysis"

Dear Brian, Thank you for contacting me and requesting that I provide you with my expert opinion as to whether your drum loop Aparthenonia is a copy of, or is based on a digital manipulation of, the plaintiff's work, "Funky Drummer II." Although I have never previously served as an expert witness by deposition or at trial in a case such as this, I believe that I am particularly qualified to provide you with a definitive comparitive analysis of the two works. I base this belief on my unique experience and expertise in the area of Computer Music, Digital Sampling, Synthesis, Sound Design, and Digital Signal Processing, plus my work and publications associated with the premiere research tool for Computer Music ­ Csound; and especially my PhD. dissertation research in FFT-based Digital Signal Analysis and Resynthesis. I have attached a copy of my resumé to further support my expertise and elaborate some on my extensive background by outlining some additional experience and credentials. I will provide a list of my publications under separate cover, but I note here that I am regarded internationally as one of the world's leading computer music composers, performers, researchers and teachers and I have edited and written the definitive textbook in the field ­ The Csound Book ­ published by MIT Press that is used to teach musicians, engineers, and computer scientists, the fundamentals of digital signal processing at universities and conservatories around the world. Furthermore, I have another defining textbook in the works for MIT Press that will be released in the winter of 2007 ­ The Audio Programming Book that teaches how to write the software and create the tools required to do the computer analysis that you have requested of me. I also have twenty years of teaching experience at the world's premiere conservatory of contemporary music recording and production ­ The Berklee College of Music in Boston; five years of research at one of the world's leading research labs ­ The Center for Music Experiment at UC San Diego; twenty-five years of work and extensive collaboration with the "father of computer music" Dr. Max Mathews at both Bell Laboratories and Stanford University; twenty-one years of work on Csound: The Universal Software Synthesis and Signal Processing Language with computer music pioneer ­ Dr. Barry Vercoe, at the MIT Media Lab in Boston; computer music research at IBM in New York (resulting in several patents) and Interval Research in California (resulting in several new synthesis technologies and patents). In preparing this report, I relied primarily on the .mp3 files Aparthenonia and Funky Drummer II that you provided me. I also reviewed the following documents for background on the case:

* Plaintiffs' Second Amended complaint * Defendant's 6/30/05 memorandum in support of defendants' motion for summary judgment and supporting documentation (including Ricigliano, Moody and Transeau declarations with attachments) * 7/22/05 Plaintiffs' Opposition to summary judgment (including Rodriguez and Ritter declarations) *10/26/05 Order on summary judgment motion

My compensation for this assignment is under discussion and has not yet been finally determined. To do my comparative analysis of the two drum-loops, I used specialized Fast Fourier Transform (FFT-based) spectral analysis algorithms from the following three digital audio research editing/processing/visualization tools for the Macintosh computer: Spear, WaveSurfer, and Audacity. A Fourier-Transform converts a time-domain representation/display (as illustrated by waveform analysis) of a sound (the physical pressure wave that we experience) into a frequency-domain representation (showing the unique timbre, spectrum, "color") of a sound (the unique frequency signature of a sound that we perceive). Thus, an FFT Analysis will reveal those characteristic features of a sound that define it as being unique. FFT-analysis is the equivalent of DNA testing for audio. The tool itself functions as a sonic microscope. It reveals, documents, and details all the hidden inner complexity that give every sound its unique fingerprint and individuality. Whereas a waveform analysis provides us with a useful general composite view of the rhythm and overall amplitude of a combined sound event, an FFT analysis will separate out all the components in a complex sound event and show how they evolve in time and contribute to make up the sound that we identify as unique. (Fourier was the French mathematician who proved that any complex sound could be deconstructed and reconstructed via a sum of harmonics (or sine waves). His mathematical model parallels how the cochlea in the inner ear translates the physical pressure wave that moves the eardrum, into discrete frequencies that stimulate particular receptors along the cochlea that are transmitted and mapped in the brain as multi-dimensional spectral images ­ what the Fourier Transform does on a computer very closely models what happens in our inner ear and in our brains. I like to explain it to my students as follows ­ We experience sound in the Time-Domain (waveform view), but we perceive sound in the Frequency-Domain (Fourier view). Whereas, a waveform analysis can be used to show that these two rather commonplace and mundane drum patterns at issue here might have some similarities, an FFT analysis will show us that the sounds that constitute these two drum loops are totally unique. A carefully tuned and equivalently set FFT-Analysis will reveal the unique DNA of any and every sound. To show the actual tone-colors and timbres, I used a Sonogram-view an FFT-view and a Frequency Analysis view. The sonogram will be used to compare the one-bar patterns over time with the X-axis showing spectral evolution over time and the Y-axis showing the unique frequency content as it evolves over time. The Fourier-view will represent frequency on the X-axis and show the detailed number of harmonics, and the amplitude of these frequency components on the Y-axis. The Frequency Analysis view shows an overall unique visual contour in which the X-axis represents frequency, and the Y-axis represent amplitude. Thus, differences in the overall shapes or contours correspond to differences in the sound. Numerical output of the analysis will also show that "the numbers" ­ which show amplitude, frequency, and analysis band are very different ­ and thus so too are the sounds. I have also done some Pitch-tracking, which shows that the pitches of the percussions instruments are unique as well. Finally, isolating individual beats and comparing them, shows that in general, there is a great deal "more" spectral information in Brian Transeau's drum-loop and thus more unique content as well. The process I used is as follows. I converted the .mp3 version of each drum-loop into a more professional .aif format. Then I isolated one bar of each drumloop. Then I split the stereo files into mono files and analyzed the same single channel from each file. Then I edited out and isolated individual beats for more detailed comparison. Once these source materials were prepared for analysis I create the following tables: 1. The first view is a complete sonograms of each file using WaveSurfer which produces a grey-scale composites whose shading illustrates the unique amplitude of each spectral component/band (Figure 1) 2. The second set of figures (Figures 2 ­ 5) use WaveSurfer's spectral and waveform views to compare individual beats of both works. 3. The third set of figures (Figures 6 ­ 11) use Spear to view the entire 1-bar pattern of both works and use frequency lines to clearly indicate the unique life, death and trajectory of each frequency/spectral component over time. 4. Figures 12 and 13 show some of the data analysis from Spear which indicates that the partials that constitute each .mpe file are themselves unique in number, duration, and size. 5. Figure 14 shows the setting used in Spear to do the analysis and result in this data set. 6. Figures 15 ­ 22 use Spear's sonogram view to show and compare the unique contours of the lower frequency
Boulanger

2: "Vargas v. Pfizer, Inc. et al., SDNY Cause No. 04-CV-9772 (WHP) - Expert opinion and FFT Analysis"

components of individual beats in each .mp3 file. 7. Figure 23 uses the program Audacity to superimpose the Waveform and Sonogram views of the entire 1-bar loop of both .mpe files. Note the unique shading and streaks in each that indicate unique frequency content. 8. Figure 24 uses Audacity to superimpose the Waveform and Pitch Analysis views of the entire 1-bar loop of both files. Although faint, you can see that there is unique pitch content in each of these soundfiles. 9. Figures 25 and 26 use enhanced autocorrelation in Audacity (which builds up dynamic multiple bandpassbandreject filters that pass frequencies with continuous energy and reject frequencies without continuous energy and therefore allows the pitch to pass freely while blocking the hiss, clicks, and ticks of the drums and thus allowing us to better isolate, focus upon and compare the unique pitch-content of each of the one-bar drumloops. Clearly they are unique and show unique overall pitch content. 10. Figures 27 and 28 are text outputs of the actual numerical data uses to draw the plots show in figures 25 and 26. In the three columns, we see the time, frequency, and amplitude of each spectral component. Comparing the same time point in figure 27 to that time point in figure 28 will reveal a difference in amplitude and thus show that they are unique. Likewise, comparing the same frequency values will show that they appear at unique timings and have unique amplitudes and are thus unique. 11. Finally, figures 29 ­ 36 use Audacity to do a comparative frequency analysis of each beat of the two soundfiles. These unique overall shapes (referred to as their spectral envelopes or signatures) show unique and different spectral content for each beat of each soundfile.

Fig1. WaveSurfer Spectrum of 1-bar loop (Aparthenonia on top, Funky Drummer on bottom ­ Note Different Spectral Content)

Boulanger

3: "Vargas v. Pfizer, Inc. et al., SDNY Cause No. 04-CV-9772 (WHP) - Expert opinion and FFT Analysis"

Fig2. WaveSurfer Spectrum of beat 1 (Aparthenonia on top, Funky Drummer on bottom ­ Note Different Spectral Content)

Fig3. WaveSurfer Spectrum of beat 2 (Aparthenonia on top, Funky Drummer on bottom ­ Note Different Spectral Content)

Boulanger

4: "Vargas v. Pfizer, Inc. et al., SDNY Cause No. 04-CV-9772 (WHP) - Expert opinion and FFT Analysis"

Fig4. WaveSurfer Spectrum of beat 3 (Aparthenonia on top, Funky Drummer on bottom ­ Note Different Spectral Content)

Fig5. WaveSurfer Spectrum of beat 4 (Aparthenonia on top, Funky Drummer on bottom ­ Note Different Spectral Content)

Boulanger

5: "Vargas v. Pfizer, Inc. et al., SDNY Cause No. 04-CV-9772 (WHP) - Expert opinion and FFT Analysis"

Fig6. Spear Sonogram 1-bar Loop (Aparthenonia Lower Frequency Content)

Boulanger

6: "Vargas v. Pfizer, Inc. et al., SDNY Cause No. 04-CV-9772 (WHP) - Expert opinion and FFT Analysis"

Fig7. Spear Sonogram 1-bar Loop (Funky Drummer Lower Frequency Content)

Boulanger

7: "Vargas v. Pfizer, Inc. et al., SDNY Cause No. 04-CV-9772 (WHP) - Expert opinion and FFT Analysis"

Fig8. Spear Sonogram 1-bar Loop (Aparthenonia Mid-High Frequency Content)

Boulanger

8: "Vargas v. Pfizer, Inc. et al., SDNY Cause No. 04-CV-9772 (WHP) - Expert opinion and FFT Analysis"

Fig9. Spear Sonogram 1-bar Loop (Funky Drummer Mid-High Frequency Content)

Boulanger

9: "Vargas v. Pfizer, Inc. et al., SDNY Cause No. 04-CV-9772 (WHP) - Expert opinion and FFT Analysis"

Fig10. Spear Sonogram 1-bar Loop (Aparthenonia High Frequency Content)

Boulanger

10: "Vargas v. Pfizer, Inc. et al., SDNY Cause No. 04-CV-9772 (WHP) - Expert opinion and FFT Analysis"

Fig11. Spear Sonogram 1-bar Loop (Funky Drummer High Frequency Content)

Fig12. Spear Console 1-bar Loop (Aparthenonia DATA)

Fig13. Spear Console 1-bar Loop (Funky Drummer DATA)

Boulanger

11: "Vargas v. Pfizer, Inc. et al., SDNY Cause No. 04-CV-9772 (WHP) - Expert opinion and FFT Analysis"

Fig14. Spear Sonogram (Analysis Settings)

Boulanger

12: "Vargas v. Pfizer, Inc. et al., SDNY Cause No. 04-CV-9772 (WHP) - Expert opinion and FFT Analysis"

Fig15. Spear Sonogram Beat 1 (Aparthenonia) Boulanger

13: "Vargas v. Pfizer, Inc. et al., SDNY Cause No. 04-CV-9772 (WHP) - Expert opinion and FFT Analysis"

Fig16. Spear Sonogram Beat 1 (Funky Drummer) Boulanger

14: "Vargas v. Pfizer, Inc. et al., SDNY Cause No. 04-CV-9772 (WHP) - Expert opinion and FFT Analysis"

Fig17. Spear Sonogram Beat 2 (Aparthenonia) Boulanger

15: "Vargas v. Pfizer, Inc. et al., SDNY Cause No. 04-CV-9772 (WHP) - Expert opinion and FFT Analysis"

Fig18. Spear Sonogram Beat 2 (Funky Drummer)

Boulanger

16: "Vargas v. Pfizer, Inc. et al., SDNY Cause No. 04-CV-9772 (WHP) - Expert opinion and FFT Analysis"

Fig19. Spear Sonogram Beat 3 (Aparthenonia) Boulanger

17: "Vargas v. Pfizer, Inc. et al., SDNY Cause No. 04-CV-9772 (WHP) - Expert opinion and FFT Analysis"

Fig20. Spear Sonogram Beat 3 (Funky Drummer) Boulanger

18: "Vargas v. Pfizer, Inc. et al., SDNY Cause No. 04-CV-9772 (WHP) - Expert opinion and FFT Analysis"

Fig21. Spear Sonogram Beat 4 (Aparthenonia) Boulanger

19: "Vargas v. Pfizer, Inc. et al., SDNY Cause No. 04-CV-9772 (WHP) - Expert opinion and FFT Analysis"

Fig22. Spear Sonogram Beat 4 (Funky Drummer) Boulanger

20: "Vargas v. Pfizer, Inc. et al., SDNY Cause No. 04-CV-9772 (WHP) - Expert opinion and FFT Analysis"

Fig23. Audacity Waveform & Spectrum 1-bar Loop (Aparthenonia above Funky Drummer)

Fig24. Audacity Waveform & Pitch 1-bar Loop (Aparthenonia above Funky Drummer)

Boulanger

21: "Vargas v. Pfizer, Inc. et al., SDNY Cause No. 04-CV-9772 (WHP) - Expert opinion and FFT Analysis"

Fig25. Audacity Enhanced Correlation Frequency Analysis 1-bar Loop (Aparthenonia)

Fig26. Audacity Enhanced Correlation Frequency Analysis 1-bar Loop (Funky Drummer)

Boulanger

22: "Vargas v. Pfizer, Inc. et al., SDNY Cause No. 04-CV-9772 (WHP) - Expert opinion and FFT Analysis"

Lag (seconds) 0.000023 0.000045 0.000068 0.000091 0.000113 0.000136 0.000159 0.000181 0.000204 0.000227 0.000249 0.000272 0.000295 0.000317 0.000340 0.000363 0.000385 0.000408 0.000431 0.000454 0.000476 0.000499 0.000522 0.000544 0.000567 0.000590 0.000612 0.000635 0.000658 0.000680 0.000703 0.000726 0.000748 0.000771 0.000794 0.000816 0.000839 0.000862 0.000884 0.000907 0.000930 0.000952 0.000975 0.000998 0.001020 0.001043 0.001066 0.001088 0.001111 0.001134 0.001156 0.001179 0.001202 0.001224 0.001247 0.001270 0.001293 0.001315 0.001338 0.001361 0.001383 0.001406 0.001429 0.001451 0.001474 Boulanger 23:

Frequency (Hz) Level 1.000000 0.000000 0.500000 0.000000 0.333333 0.000000 0.250000 0.000000 0.200000 0.000000 0.166667 0.000000 0.142857 0.000000 0.125000 0.000000 0.111111 0.000000 0.100000 0.000000 0.090909 21.553040 0.083333 20.215500 0.076923 0.759315 0.071429 0.000000 0.066667 0.000000 0.062500 3.803909 0.058824 6.605278 0.055556 0.634415 0.052632 0.000000 0.050000 3.611328 0.047619 0.000000 0.045455 0.000000 0.043478 0.000000 0.041667 0.000000 0.040000 0.000000 0.038462 0.000000 0.037037 0.000000 0.035714 0.000000 0.034483 0.000000 0.033333 0.000000 0.032258 0.000000 0.031250 0.000000 0.030303 0.000000 0.029412 0.000000 0.028571 0.000000 0.027778 0.000000 0.027027 0.000000 0.026316 0.000000 0.025641 0.000000 0.025000 0.000000 0.024390 0.000000 0.023810 0.000000 0.023256 0.000000 0.022727 0.000000 0.022222 0.000000 0.021739 0.000000 0.021277 0.000000 0.020833 0.000000 0.020408 0.000000 0.020000 0.000000 0.019608 0.000000 0.019231 0.000000 0.018868 0.000000 0.018519 0.000000 0.018182 0.000000 0.017857 0.000000 0.017544 0.000000 0.017241 0.000000 0.016949 0.000000 0.016667 0.000000 0.016393 0.000000 0.016129 0.000000 0.015873 0.000000 0.015625 0.000000 0.015385 0.000000 "Vargas v. Pfizer, Inc. et al., SDNY Cause No. 04-CV-9772 (WHP) - Expert opinion and FFT Analysis"

0.001497 0.001519 0.001542 0.001565 0.001587 0.001610 0.001633 0.001655 0.001678 0.001701 0.001723 0.001746 0.001769 0.001791 0.001814 0.001837 0.001859 0.001882 0.001905 0.001927 0.001950 0.001973 0.001995 0.002018 0.002041 0.002063 0.002086 0.002109 0.002132 0.002154 0.002177 0.002200 0.002222 0.002245 0.002268 0.002290 0.002313 0.002336 0.002358 0.002381 0.002404 0.002426 0.002449 0.002472 0.002494 0.002517 0.002540 0.002562 0.002585 0.002608 0.002630 0.002653 0.002676 0.002698 0.002721 0.002744 0.002766 0.002789 0.002812 0.002834 0.002857 0.002880 0.002902 0.002925 0.002948 0.002971 Boulanger

24:

0.015152 0.000000 0.014925 0.000000 0.014706 0.000000 0.014493 0.000000 0.014286 0.000000 0.014085 0.000000 0.013889 0.000000 0.013699 0.000000 0.013514 0.000000 0.013333 0.000000 0.013158 0.000000 0.012987 0.000000 0.012821 0.000000 0.012658 0.000000 0.012500 0.000000 0.012346 0.000000 0.012195 0.000000 0.012048 0.000000 0.011905 0.000000 0.011765 0.000000 0.011628 0.000000 0.011494 0.000000 0.011364 0.000000 0.011236 0.000000 0.011111 0.000000 0.010989 0.000000 0.010870 0.000000 0.010753 0.000000 0.010638 0.000000 0.010526 0.000000 0.010417 0.000000 0.010309 0.000000 0.010204 0.000000 0.010101 0.000000 0.010000 0.000000 0.009901 0.000000 0.009804 0.000000 0.009709 0.000000 0.009615 0.000000 0.009524 -0.000000 0.009434 0.000000 0.009346 0.000000 0.009259 0.000000 0.009174 0.000000 0.009091 0.000000 0.009009 0.000000 0.008929 0.000000 0.008850 0.000000 0.008772 0.000000 0.008696 0.000000 0.008621 0.000000 0.008547 0.000000 0.008475 0.000000 0.008403 -0.000000 0.008333 0.000000 0.008264 -0.000000 0.008197 0.000000 0.008130 -0.000000 0.008065 0.000000 0.008000 -0.000000 0.007937 0.000000 0.007874 -0.000000 0.007812 0.000000 0.007752 -0.000000 0.007692 0.000000 0.007634 -0.000000 "Vargas v. Pfizer, Inc. et al., SDNY Cause No. 04-CV-9772 (WHP) - Expert opinion and FFT Analysis"

0.002993 0.003016 0.003039 0.003061 0.003084 0.003107 0.003129 0.003152 0.003175 0.003197 0.003220 0.003243 0.003265 0.003288 0.003311 0.003333 0.003356 0.003379 0.003401 0.003424 0.003447 0.003469 0.003492 0.003515 0.003537 0.003560 0.003583 0.003605 0.003628 0.003651 0.003673 0.003696 0.003719 0.003741 0.003764 0.003787 0.003810 0.003832 0.003855 0.003878 0.003900 0.003923 0.003946 0.003968 0.003991 0.004014 0.004036 0.004059 0.004082 0.004104 0.004127 0.004150 0.004172 0.004195 0.004218 0.004240 0.004263 0.004286 0.004308 0.004331 0.004354 0.004376 0.004399 0.004422 0.004444 0.004467 Boulanger

25:

0.007576 0.000000 0.007519 -0.000000 0.007463 0.000000 0.007407 -0.000000 0.007353 0.000000 0.007299 -0.000000 0.007246 0.000000 0.007194 -0.000000 0.007143 0.000000 0.007092 -0.000000 0.007042 0.000000 0.006993 -0.000000 0.006944 0.000000 0.006897 -0.000000 0.006849 0.000000 0.006803 -0.000000 0.006757 0.000000 0.006711 -0.000000 0.006667 0.000000 0.006623 -0.000000 0.006579 0.000000 0.006536 -0.000000 0.006494 0.000000 0.006452 -0.000000 0.006410 0.000000 0.006369 -0.000000 0.006329 0.000000 0.006289 -0.000000 0.006250 0.000000 0.006211 -0.000000 0.006173 0.000000 0.006135 -0.000000 0.006098 0.000000 0.006061 -0.000000 0.006024 0.000000 0.005988 -0.000000 0.005952 0.000000 0.005917 -0.000000 0.005882 0.000000 0.005848 -0.000000 0.005814 0.000000 0.005780 -0.000000 0.005747 0.000000 0.005714 -0.000000 0.005682 0.000000 0.005650 -0.000000 0.005618 0.000000 0.005587 -0.000000 0.005556 0.000000 0.005525 -0.000000 0.005495 0.000000 0.005464 -0.000000 0.005435 0.000000 0.005405 -0.000000 0.005376 0.000000 0.005348 -0.000000 0.005319 0.000000 0.005291 -0.000000 0.005263 0.000000 0.005236 -0.000000 0.005208 0.000000 0.005181 -0.000000 0.005155 0.000000 0.005128 -0.000000 0.005102 0.000000 0.005076 -0.000000 "Vargas v. Pfizer, Inc. et al., SDNY Cause No. 04-CV-9772 (WHP) - Expert opinion and FFT Analysis"

0.004490 0.004512 0.004535 0.004558 0.004580 0.004603 0.004626 0.004649 0.004671 0.004694 0.004717 0.004739 0.004762 0.004785 0.004807 0.004830 0.004853 0.004875 0.004898 0.004921 0.004943 0.004966 0.004989 0.005011 0.005034 0.005057 0.005079 0.005102 0.005125 0.005147 0.005170 0.005193 0.005215 0.005238 0.005261 0.005283 0.005306 0.005329 0.005351 0.005374 0.005397 0.005420 0.005442 0.005465 0.005488 0.005510 0.005533 0.005556 0.005578 0.005601 0.005624 0.005646 0.005669 0.005692 0.005714 0.005737 0.005760 0.005782 0.005805 0.005828 0.005850 0.005873 0.005896 0.005918 0.005941 0.005964 Boulanger

26:

0.005051 0.000000 0.005025 -0.000000 0.005000 0.000000 0.004975 -0.000000 0.004950 0.000000 0.004926 -0.000000 0.004902 0.000000 0.004878 -0.000000 0.004854 0.000000 0.004831 -0.000000 0.004808 0.000000 0.004785 -0.000000 0.004762 0.000000 0.004739 -0.000000 0.004717 0.000000 0.004695 -0.000000 0.004673 0.000000 0.004651 -0.000000 0.004630 0.000000 0.004608 -0.000000 0.004587 0.000000 0.004566 -0.000000 0.004545 0.000000 0.004525 -0.000000 0.004505 0.000000 0.004484 -0.000000 0.004464 0.000000 0.004444 -0.000000 0.004425 0.000000 0.004405 -0.000000 0.004386 0.000000 0.004367 -0.000000 0.004348 0.000000 0.004329 -0.000000 0.004310 0.000000 0.004292 -0.000000 0.004274 0.000000 0.004255 -0.000000 0.004237 0.000000 0.004219 -0.000000 0.004202 0.000000 0.004184 -0.000000 0.004167 0.000000 0.004149 -0.000000 0.004132 0.000000 0.004115 -0.000000 0.004098 0.000000 0.004082 -0.000000 0.004065 0.000000 0.004049 -0.000000 0.004032 0.000000 0.004016 -0.000000 0.004000 0.000000 0.003984 -0.000000 0.003968 0.000000 0.003953 -0.000000 0.003937 0.000000 0.003922 -0.000000 0.003906 0.000000 0.003891 -0.000000 0.003876 0.000000 0.003861 -0.000000 0.003846 0.000000 0.003831 -0.000000 0.003817 0.000000 0.003802 -0.000000 "Vargas v. Pfizer, Inc. et al., SDNY Cause No. 04-CV-9772 (WHP) - Expert opinion and FFT Analysis"

0.005986 0.006009 0.006032 0.006054 0.006077 0.006100 0.006122 0.006145 0.006168 0.006190 0.006213 0.006236 0.006259 0.006281 0.006304 0.006327 0.006349 0.006372 0.006395 0.006417 0.006440 0.006463 0.006485 0.006508 0.006531 0.006553 0.006576 0.006599 0.006621 0.006644 0.006667 0.006689 0.006712 0.006735 0.006757 0.006780 0.006803 0.006825 0.006848 0.006871 0.006893 0.006916 0.006939 0.006961 0.006984 0.007007 0.007029 0.007052 0.007075 0.007098 0.007120 0.007143 0.007166 0.007188 0.007211 0.007234 0.007256 0.007279 0.007302 0.007324 0.007347 0.007370 0.007392 0.007415 0.007438 0.007460 Boulanger

27:

0.003788 0.000000 0.003774 -0.000000 0.003759 0.000000 0.003745 -0.000000 0.003731 0.000000 0.003717 -0.000000 0.003704 0.000000 0.003690 -0.000000 0.003676 0.000000 0.003663 -0.000000 0.003650 0.000000 0.003636 -0.000000 0.003623 0.000000 0.003610 -0.000000 0.003597 0.000000 0.003584 -0.000000 0.003571 0.000000 0.003559 -0.000000 0.003546 0.000000 0.003534 -0.000000 0.003521 0.000000 0.003509 -0.000000 0.003497 0.000000 0.003484 -0.000000 0.003472 0.000000 0.003460 -0.000000 0.003448 0.000000 0.003436 -0.000000 0.003425 0.030350 0.003413 0.720607 0.003401 0.000000 0.003390 -0.000000 0.003378 0.000000 0.003367 -0.000000 0.003356 0.000000 0.003344 -0.000000 0.003333 0.000000 0.003322 -0.000000 0.003311 0.000000 0.003300 -0.000000 0.003289 0.000000 0.003279 -0.000000 0.003268 0.000000 0.003257 -0.000000 0.003247 0.000000 0.003236 -0.000000 0.003226 0.000000 0.003215 -0.000000 0.003205 0.000000 0.003195 -0.000000 0.003185 0.000000 0.003175 -0.000000 0.003165 0.000000 0.003155 -0.000000 0.003145 0.000000 0.003135 -0.000000 0.003125 0.000000 0.003115 -0.000000 0.003106 0.000000 0.003096 -0.000000 0.003086 0.000000 0.003077 -0.000000 0.003067 0.000000 0.003058 -0.000000 0.003049 0.000000 0.003040 -0.000000 "Vargas v. Pfizer, Inc. et al., SDNY Cause No. 04-CV-9772 (WHP) - Expert opinion and FFT Analysis"

0.007483 0.007506 0.007528 0.007551 0.007574 0.007596 0.007619 0.007642 0.007664 0.007687 0.007710 0.007732 0.007755 0.007778 0.007800 0.007823 0.007846 0.007868 0.007891 0.007914 0.007937 0.007959 0.007982 0.008005 0.008027 0.008050 0.008073 0.008095 0.008118 0.008141 0.008163 0.008186 0.008209 0.008231 0.008254 0.008277 0.008299 0.008322 0.008345 0.008367 0.008390 0.008413 0.008435 0.008458 0.008481 0.008503 0.008526 0.008549 0.008571 0.008594 0.008617 0.008639 0.008662 0.008685 0.008707 0.008730 0.008753 0.008776 0.008798 0.008821 0.008844 0.008866 0.008889 0.008912 0.008934 0.008957 Boulanger

28:

0.003030 0.000000 0.003021 -0.000000 0.003012 0.000000 0.003003 -0.000000 0.002994 0.000000 0.002985 -0.000000 0.002976 0.000000 0.002967 -0.000000 0.002959 0.000000 0.002950 -0.000000 0.002941 0.000000 0.002933 -0.000000 0.002924 0.000000 0.002915 -0.000000 0.002907 0.000000 0.002899 -0.000000 0.002890 0.000000 0.002882 0.331496 0.002874 0.000000 0.002865 -0.000000 0.002857 0.000000 0.002849 -0.000000 0.002841 0.608095 0.002833 -0.000000 0.002825 0.000000 0.002817 -0.000000 0.002809 0.000000 0.002801 -0.000000 0.002793 0.655745 0.002786 2.066183 0.002778 1.835125 0.002770 -0.000000 0.002762 0.000000 0.002755 -0.000000 0.002747 0.000000 0.002740 -0.000000 0.002732 0.000000 0.002725 -0.000000 0.002717 0.463953 0.002710 -0.000000 0.002703 0.000000 0.002695 -0.000000 0.002688 0.000000 0.002681 -0.000000 0.002674 0.000000 0.002667 2.051878 0.002660 0.000000 0.002653 -0.000000 0.002646 0.000000 0.002639 -0.000000 0.002632 0.000000 0.002625 -0.000000 0.002618 0.000000 0.002611 -0.000000 0.002604 0.000000 0.002597 -0.000000 0.002591 0.000000 0.002584 1.412363 0.002577 0.000000 0.002571 -0.000000 0.002564 0.000000 0.002558 -0.000000 0.002551 1.779446 0.002545 4.637920 0.002538 3.199990 0.002532 1.678653 "Vargas v. Pfizer, Inc. et al., SDNY Cause No. 04-CV-9772 (WHP) - Expert opinion and FFT Analysis"

0.008980 0.009002 0.009025 0.009048 0.009070 0.009093 0.009116 0.009138 0.009161 0.009184 0.009206 0.009229 0.009252 0.009274 0.009297 0.009320 0.009342 0.009365 0.009388 0.009410 0.009433 0.009456 0.009478 0.009501 0.009524 0.009546 0.009569 0.009592 0.009615 0.009637 0.009660 0.009683 0.009705 0.009728 0.009751 0.009773 0.009796 0.009819 0.009841 0.009864 0.009887 0.009909 0.009932 0.009955 0.009977 0.010000 0.010023 0.010045 0.010068 0.010091 0.010113 0.010136 0.010159 0.010181 0.010204 0.010227 0.010249 0.010272 0.010295 0.010317 0.010340 0.010363 0.010385 0.010408 0.010431 0.010454 Boulanger

29:

0.002525 2.088795 0.002519 2.363193 0.002513 1.266256 0.002506 -0.000000 0.002500 2.719098 0.002494 7.756382 0.002488 4.127491 0.002481 1.837810 0.002475 4.841058 0.002469 3.711902 0.002463 1.286673 0.002457 0.594875 0.002451 0.000000 0.002445 0.304012 0.002439 2.858684 0.002433 3.015993 0.002427 0.429845 0.002421 -0.000000 0.002415 0.000000 0.002410 1.522691 0.002404 2.656686 0.002398 0.696606 0.002392 0.000000 0.002387 -0.000000 0.002381 0.000000 0.002375 -0.000000 0.002370 2.894464 0.002364 3.453092 0.002358 2.339815 0.002353 2.558439 0.002347 1.485211 0.002342 0.084416 0.002336 0.158762 0.002331 2.922977 0.002326 4.784974 0.002320 4.644542 0.002315 3.335803 0.002309 0.286866 0.002304 0.000000 0.002299 -0.000000 0.002294 0.000000 0.002288 -0.000000 0.002283 0.000000 0.002278 -0.000000 0.002273 0.701921 0.002268 1.547218 0.002262 0.000000 0.002257 -0.000000 0.002252 0.000000 0.002247 -0.000000 0.002242 0.000000 0.002237 -0.000000 0.002232 0.000000 0.002227 -0.000000 0.002222 0.000000 0.002217 -0.000000 0.002212 0.000000 0.002208 -0.000000 0.002203 0.000000 0.002198 -0.000000 0.002193 0.000000 0.002188 -0.000000 0.002183 0.000000 0.002179 -0.000000 0.002174 0.000000 0.002169 -0.000000 "Vargas v. Pfizer, Inc. et al., SDNY Cause No. 04-CV-9772 (WHP) - Expert opinion and FFT Analysis"

0.010476 0.010499 0.010522 0.010544 0.010567 0.010590 0.010612 0.010635 0.010658 0.010680 0.010703 0.010726 0.010748 0.010771 0.010794 0.010816 0.010839 0.010862 0.010884 0.010907 0.010930 0.010952 0.010975 0.010998 0.011020 0.011043 0.011066 0.011088 0.011111 0.011134 0.011156 0.011179 0.011202 0.011224 0.011247 0.011270 0.011293 0.011315 0.011338 0.011361 0.011383 0.011406 0.011429 0.011451 0.011474 0.011497 0.011519 0.011542 0.011565 0.011587 0.011610 0.011633 0.011655 0.011678 0.011701 0.011723 0.011746 0.011769 0.011791 0.011814 0.011837 0.011859 0.011882 0.011905 0.011927 0.011950 Boulanger

30:

0.002165 0.000000 0.002160 -0.000000 0.002155 0.000000 0.002151 -0.000000 0.002146 0.000000 0.002141 -0.000000 0.002137 0.000000 0.002132 -0.000000 0.002128 0.000000 0.002123 -0.000000 0.002119 0.000000 0.002114 -0.000000 0.002110 0.000000 0.002105 -0.000000 0.002101 0.000000 0.002096 -0.000000 0.002092 0.000000 0.002088 -0.000000 0.002083 0.000000 0.002079 -0.000000 0.002075 0.000000 0.002070 -0.000000 0.002066 0.000000 0.002062 -0.000000 0.002058 0.000000 0.002053 -0.000000 0.002049 0.000000 0.002045 -0.000000 0.002041 0.000000 0.002037 -0.000000 0.002033 0.000000 0.002028 -0.000000 0.002024 0.000000 0.002020 -0.000000 0.002016 0.000000 0.002012 -0.000000 0.002008 0.000000 0.002004 -0.000000 0.002000 0.000000 0.001996 -0.000000 0.001992 0.000000 0.001988 -0.000000 0.001984 0.000000 0.001980 -0.000000 0.001976 0.000000 0.001972 -0.000000 0.001969 0.000000 0.001965 0.499373 0.001961 0.000000 0.001957 -0.000000 0.001953 0.000000 0.001949 -0.000000 0.001946 0.000000 0.001942 -0.000000 0.001938 0.000000 0.001934 -0.000000 0.001931 1.356868 0.001927 4.854334 0.001923 4.315751 0.001919 1.718317 0.001916 0.000000 0.001912 -0.000000 0.001908 0.000000 0.001905 0.936441 0.001901 2.429510 0.001898 2.214805 "Vargas v. Pfizer, Inc. et al., SDNY Cause No. 04-CV-9772 (WHP) - Expert opinion and FFT Analysis"

0.011973 0.011995 0.012018 0.012041 0.012063 0.012086 0.012109 0.012132 0.012154 0.012177 0.012200 0.012222 0.012245 0.012268 0.012290 0.012313 0.012336 0.012358 0.012381 0.012404 0.012426 0.012449 0.012472 0.012494 0.012517 0.012540 0.012562 0.012585 0.012608 0.012630 0.012653 0.012676 0.012698 0.012721 0.012744 0.012766 0.012789 0.012812 0.012834 0.012857 0.012880 0.012902 0.012925 0.012948 0.012971 0.012993 0.013016 0.013039 0.013061 0.013084 0.013107 0.013129 0.013152 0.013175 0.013197 0.013220 0.013243 0.013265 0.013288 0.013311 0.013333 0.013356 0.013379 0.013401 0.013424 0.013447 Boulanger

31:

0.001894 0.892802 0.001890 -0.000000 0.001887 0.000000 0.001883 -0.000000 0.001880 0.000000 0.001876 -0.000000 0.001873 0.000000 0.001869 0.025088 0.001866 1.994829 0.001862 3.205456 0.001859 2.777256 0.001855 2.714776 0.001852 1.461185 0.001848 0.395720 0.001845 1.759557 0.001842 2.951923 0.001838 2.695057 0.001835 3.505614 0.001832 5.741745 0.001828 7.321740 0.001825 7.582151 0.001821 6.061100 0.001818 4.741284 0.001815 3.527966 0.001812 2.788777 0.001808 4.519060 0.001805 4.264087 0.001802 1.632328 0.001799 1.228737 0.001795 1.463804 0.001792 2.220574 0.001789 4.607594 0.001786 4.977704 0.001783 3.510398 0.001779 3.565978 0.001776 3.363751 0.001773 2.296714 0.001770 3.110151 0.001767 3.916647 0.001764 2.927113 0.001761 2.402445 0.001757 3.132883 0.001754 4.282025 0.001751 4.805913 0.001748 4.724681 0.001745 4.125867 0.001742 3.765930 0.001739 4.530559 0.001736 5.425923 0.001733 6.530627 0.001730 6.867395 0.001727 4.325947 0.001724 2.271319 0.001721 3.287029 0.001718 6.055679 0.001715 8.705225 0.001712 8.019490 0.001709 4.341346 0.001706 1.849572 0.001704 0.790190 0.001701 0.628326 0.001698 -0.000000 0.001695 0.000000 0.001692 0.183877 0.001689 1.495579 0.001686 -0.000000 "Vargas v. Pfizer, Inc. et al., SDNY Cause No. 04-CV-9772 (WHP) - Expert opinion and FFT Analysis"

0.013469 0.013492 0.013515 0.013537 0.013560 0.013583 0.013605 0.013628 0.013651 0.013673 0.013696 0.013719 0.013741 0.013764 0.013787 0.013810 0.013832 0.013855 0.013878 0.013900 0.013923 0.013946 0.013968 0.013991 0.014014 0.014036 0.014059 0.014082 0.014104 0.014127 0.014150 0.014172 0.014195 0.014218 0.014240 0.014263 0.014286 0.014308 0.014331 0.014354 0.014376 0.014399 0.014422 0.014444 0.014467 0.014490 0.014512 0.014535 0.014558 0.014580 0.014603 0.014626 0.014649 0.014671 0.014694 0.014717 0.014739 0.014762 0.014785 0.014807 0.014830 0.014853 0.014875 0.014898 0.014921 0.014943 Boulanger

32:

0.001684 0.000000 0.001681 0.861865 0.001678 1.096002 0.001675 0.013170 0.001672 0.000000 0.001669 0.507202 0.001667 1.663264 0.001664 1.978921 0.001661 0.115023 0.001658 -0.000000 0.001656 0.055234 0.001653 0.499235 0.001650 2.110765 0.001647 3.940285 0.001645 4.165462 0.001642 4.840200 0.001639 6.204906 0.001637 7.203015 0.001634 6.864990 0.001631 4.430894 0.001629 3.072311 0.001626 2.894165 0.001623 3.616418 0.001621 4.441782 0.001618 4.741677 0.001616 4.617462 0.001613 3.583952 0.001610 2.733568 0.001608 4.090377 0.001605 6.580335 0.001603 6.149681 0.001600 4.826411 0.001597 3.966119 0.001595 3.205339 0.001592 3.423096 0.001590 2.907916 0.001587 2.983257 0.001585 3.743700 0.001582 3.890339 0.001580 4.677491 0.001577 5.615147 0.001575 5.518929 0.001572 4.613779 0.001570 4.550924 0.001567 5.604510 0.001565 5.620639 0.001563 5.184771 0.001560 5.056959 0.001558 5.203800 0.001555 4.194970 0.001553 3.315416 0.001550 3.956429 0.001548 4.400735 0.001546 4.974723 0.001543 5.874137 0.001541 5.405963 0.001538 4.419878 0.001536 4.960225 0.001534 4.826321 0.001531 3.584028 0.001529 3.572710 0.001527 3.791602 0.001524 3.301149 0.001522 3.791604 0.001520 5.605894 0.001517 6.445282 "Vargas v. Pfizer, Inc. et al., SDNY Cause No. 04-CV-9772 (WHP) - Expert opinion and FFT Analysis"

0.014966 0.014989 0.015011 0.015034 0.015057 0.015079 0.015102 0.015125 0.015147 0.015170 0.015193 0.015215 0.015238 0.015261 0.015283 0.015306 0.015329 0.015351 0.015374 0.015397 0.015420 0.015442 0.015465 0.015488 0.015510 0.015533 0.015556 0.015578 0.015601 0.015624 0.015646 0.015669 0.015692 0.015714 0.015737 0.015760 0.015782 0.015805 0.015828 0.015850 0.015873 0.015896 0.015918 0.015941 0.015964 0.015986 0.016009 0.016032 0.016054 0.016077 0.016100 0.016122 0.016145 0.016168 0.016190 0.016213 0.016236 0.016259 0.016281 0.016304 0.016327 0.016349 0.016372 0.016395 0.016417 0.016440 Boulanger

33:

0.001515 6.136918 0.001513 5.659092 0.001511 5.450059 0.001508 4.910730 0.001506 4.340757 0.001504 3.302335 0.001502 2.114852 0.001499 1.719238 0.001497 2.551761 0.001495 3.630986 0.001493 4.258947 0.001490 4.624305 0.001488 3.679489 0.001486 2.228204 0.001484 2.334379 0.001481 2.737811 0.001479 3.051713 0.001477 3.851770 0.001475 4.390267 0.001473 3.940096 0.001471 4.257960 0.001468 4.004947 0.001466 2.431141 0.001464 1.112686 0.001462 0.463080 0.001460 0.776010 0.001458 2.342703 0.001456 3.990129 0.001453 4.085196 0.001451 2.596519 0.001449 0.744969 0.001447 0.630498 0.001445 1.491628 0.001443 0.484389 0.001441 0.810620 0.001439 2.524523 0.001437 1.623435 0.001435 -0.000000 0.001433 0.000000 0.001431 -0.000000 0.001429 0.195276 0.001427 0.583048 0.001425 0.933940 0.001422 1.318214 0.001420 1.376323 0.001418 0.757218 0.001416 0.007257 0.001414 0.249780 0.001412 0.286080 0.001410 -0.000000 0.001408 0.000000 0.001406 0.749603 0.001404 1.921491 0.001403 1.218330 0.001401 1.394638 0.001399 1.181827 0.001397 0.000000 0.001395 0.000000 0.001393 0.000000 0.001391 0.000000 0.001389 0.000000 0.001387 0.000000 0.001385 0.000000 0.001383 -0.000000 0.001381 0.000000 0.001379 -0.000000 "Vargas v. Pfizer, Inc. et al., SDNY Cause No. 04-CV-9772 (WHP) - Expert opinion and FFT Analysis"

0.016463 0.016485 0.016508 0.016531 0.016553 0.016576 0.016599 0.016621 0.016644 0.016667 0.016689 0.016712 0.016735 0.016757 0.016780 0.016803 0.016825 0.016848 0.016871 0.016893 0.016916 0.016939 0.016961 0.016984 0.017007 0.017029 0.017052 0.017075 0.017098 0.017120 0.017143 0.017166 0.017188 0.017211 0.017234 0.017256 0.017279 0.017302 0.017324 0.017347 0.017370 0.017392 0.017415 0.017438 0.017460 0.017483 0.017506 0.017528 0.017551 0.017574 0.017596 0.017619 0.017642 0.017664 0.017687 0.017710 0.017732 0.017755 0.017778 0.017800 0.017823 0.017846 0.017868 0.017891 0.017914 0.017937 Boulanger

34:

0.001377 0.000000 0.001376 -0.000000 0.001374 0.000000 0.001372 -0.000000 0.001370 0.553173 0.001368 1.575709 0.001366 2.408798 0.001364 2.360337 0.001362 2.376034 0.001361 1.247967 0.001359 0.000000 0.001357 0.528015 0.001355 2.911263 0.001353 2.656713 0.001351 0.394078 0.001350 -0.000000 0.001348 0.000000 0.001346 -0.000000 0.001344 0.000000 0.001342 0.396407 0.001340 1.414532 0.001339 0.681775 0.001337 0.620630 0.001335 0.000000 0.001333 0.000000 0.001332 1.421151 0.001330 3.110968 0.001328 2.851162 0.001326 3.015875 0.001325 3.297527 0.001323 1.795864 0.001321 0.513878 0.001319 1.111261 0.001318 1.303059 0.001316 0.667004 0.001314 1.096223 0.001312 1.932258 0.001311 1.999059 0.001309 2.085066 0.001307 1.070184 0.001305 0.000000 0.001304 -0.000000 0.001302 0.332317 0.001300 0.473074 0.001299 0.000000 0.001297 -0.000000 0.001295 0.000000 0.001294 0.000000 0.001292 0.000000 0.001290 0.000000 0.001289 0.000000 0.001287 -0.000000 0.001285 0.000000 0.001284 -0.000000 0.001282 0.000000 0.001280 -0.000000 0.001279 0.000000 0.001277 0.000000 0.001276 0.000000 0.001274 0.000000 0.001272 0.000000 0.001271 0.000000 0.001269 0.000000 0.001267 0.000000 0.001266 0.000000 0.001264 0.000000 "Vargas v. Pfizer, Inc. et al., SDNY Cause No. 04-CV-9772 (WHP) - Expert opinion and FFT Analysis"

0.017959 0.017982 0.018005 0.018027 0.018050 0.018073 0.018095 0.018118 0.018141 0.018163 0.018186 0.018209 0.018231 0.018254 0.018277 0.018299 0.018322 0.018345 0.018367 0.018390 0.018413 0.018435 0.018458 0.018481 0.018503 0.018526 0.018549 0.018571 0.018594 0.018617 0.018639 0.018662 0.018685 0.018707 0.018730 0.018753 0.018776 0.018798 0.018821 0.018844 0.018866 0.018889 0.018912 0.018934 0.018957 0.018980 0.019002 0.019025 0.019048 0.019070 0.019093 0.019116 0.019138 0.019161 0.019184 0.019206 0.019229 0.019252 0.019274 0.019297 0.019320 0.019342 0.019365 0.019388 0.019410 0.019433 Boulanger

35:

0.001263 0.000000 0.001261 0.000000 0.001259 0.000000 0.001258 0.000000 0.001256 0.000000 0.001255 0.000000 0.001253 0.000000 0.001252 0.000000 0.001250 0.000000 0.001248 0.000000 0.001247 0.000000 0.001245 0.000000 0.001244 0.000000 0.001242 0.000000 0.001241 0.000000 0.001239 0.000000 0.001238 0.000000 0.001236 0.000000 0.001235 0.000000 0.001233 0.000000 0.001232 0.000000 0.001230 0.000000 0.001229 0.000000 0.001227 0.000000 0.001225 0.000000 0.001224 0.000000 0.001222 0.000000 0.001221 0.000000 0.001220 0.000000 0.001218 0.000000 0.001217 0.000000 0.001215 0.000000 0.001214 0.000000 0.001212 0.000000 0.001211 0.000000 0.001209 -0.000000 0.001208 0.000000 0.001206 0.000000 0.001205 0.000000 0.001203 0.000000 0.001202 0.000000 0.001200 0.000000 0.001199 0.000000 0.001198 0.000000 0.001196 0.000000 0.001195 -0.000000 0.001193 0.000000 0.001192 -0.000000 0.001190 0.000000 0.001189 -0.000000 0.001188 0.000000 0.001186 0.000000 0.001185 0.000000 0.001183 0.000000 0.001182 0.000000 0.001181 0.000000 0.001179 0.000000 0.001178 0.000000 0.001176 0.000000 0.001175 0.000000 0.001174 0.000000 0.001172 0.000000 0.001171 0.000000 0.001170 0.000000 0.001168 0.000000 0.001167 0.000000 "Vargas v. Pfizer, Inc. et al., SDNY Cause No. 04-CV-9772 (WHP) - Expert opinion and FFT Analysis"

0.019456 0.019478 0.019501 0.019524 0.019546 0.019569 0.019592 0.019615 0.019637 0.019660 0.019683 0.019705 0.019728 0.019751 0.019773 0.019796 0.019819 0.019841 0.019864 0.019887 0.019909 0.019932 0.019955 0.019977 0.020000 0.020023 0.020045 0.020068 0.020091 0.020113 0.020136 0.020159 0.020181 0.020204 0.020227 0.020249 0.020272 0.020295 0.020317 0.020340 0.020363 0.020385 0.020408 0.020431 0.020454 0.020476 0.020499 0.020522 0.020544 0.020567 0.020590 0.020612 0.020635 0.020658 0.020680 0.020703 0.020726 0.020748 0.020771 0.020794 0.020816 0.020839 0.020862 0.020884 0.020907 0.020930 Boulanger

36:

0.001166 0.000000 0.001164 0.000000 0.001163 0.000000 0.001161 0.000000 0.001160 0.000000 0.001159 0.000000 0.001157 0.000000 0.001156 0.000000 0.001155 0.000000 0.001153 0.000000 0.001152 0.000000 0.001151 -0.000000 0.001149 0.000000 0.001148 -0.000000 0.001147 0.000000 0.001145 -0.000000 0.001144 0.000000 0.001143 -0.000000 0.001142 0.000000 0.001140 -0.000000 0.001139 0.000000 0.001138 0.000000 0.001136 0.000000 0.001135 0.000000 0.001134 0.000000 0.001133 0.000000 0.001131 0.760966 0.001130 0.401430 0.001129 0.171665 0.001127 -0.000000 0.001126 0.275582 0.001125 1.217449 0.001124 1.233897 0.001122 0.502745 0.001121 0.265510 0.001120 0.800075 0.001119 1.024715 0.001117 0.690821 0.001116 1.016031 0.001115 1.421884 0.001114 0.584732 0.001112 -0.000000 0.001111 0.257285 0.001110 0.991919 0.001109 0.297135 0.001107 -0.000000 0.001106 0.000000 0.001105 0.023706 0.001104 0.689815 0.001103 0.881162 0.001101 0.000000 0.001100 0.125918 0.001099 1.572866 0.001098 1.180145 0.001096 0.000000 0.001095 -0.000000 0.001094 0.478009 0.001093 1.104993 0.001092 0.616622 0.001091 -0.000000 0.001089 0.000000 0.001088 -0.000000 0.001087 0.000000 0.001086 -0.000000 0.001085 0.000000 0.001083 -0.000000 "Vargas v. Pfizer, Inc. et al., SDNY Cause No. 04-CV-9772 (WHP) - Expert opinion and FFT Analysis"

0.020952 0.020975 0.020998 0.021020 0.021043 0.021066 0.021088 0.021111 0.021134 0.021156 0.021179 0.021202 0.021224 0.021247 0.021270 0.021293 0.021315 0.021338 0.021361 0.021383 0.021406 0.021429 0.021451 0.021474 0.021497 0.021519 0.021542 0.021565 0.021587 0.021610 0.021633 0.021655 0.021678 0.021701 0.021723 0.021746 0.021769 0.021791 0.021814 0.021837 0.021859 0.021882 0.021905 0.021927 0.021950 0.021973 0.021995 0.022018 0.022041 0.022063 0.022086 0.022109 0.022132 0.022154 0.022177 0.022200 0.022222 0.022245 0.022268 0.022290 0.022313 0.022336 0.022358 0.022381 0.022404 0.022426 Boulanger

37:

0.001082 0.000000 0.001081 -0.000000 0.001080 0.000000 0.001079 0.670733 0.001078 0.957052 0.001076 -0.000000 0.001075 0.207806 0.001074 1.231452 0.001073 0.891344 0.001072 0.042181 0.001071 0.368850 0.001070 0.589769 0.001068 0.000000 0.001067 -0.000000 0.001066 0.000000 0.001065 -0.000000 0.001064 0.194579 0.001063 0.577821 0.001062 0.627626 0.001060 0.913529 0.001059 0.800466 0.001058 -0.000000 0.001057 0.200410 0.001056 1.077616 0.001055 0.879951 0.001054 0.624668 0.001053 1.003232 0.001052 1.434390 0.001050 1.194049 0.001049 0.627762 0.001048 0.000000 0.001047 -0.000000 0.001046 0.000000 0.001045 0.027955 0.001044 0.000000 0.001043 -0.000000 0.001042 0.000000 0.001041 -0.000000 0.001040 0.000000 0.001038 -0.000000 0.001037 0.000000 0.001036 0.427477 0.001035 0.329204 0.001034 0.139784 0.001033 0.366731 0.001032 0.387541 0.001031 0.319853 0.001030 0.865504 0.001029 1.142160 0.001028 1.831300 0.001027 2.265506 0.001026 1.520689 0.001025 1.556800 0.001024 1.242693 0.001022 0.000000 0.001021 -0.000000 0.001020 0.000000 0.001019 -0.000000 0.001018 0.000000 0.001017 -0.000000 0.001016 0.823129 0.001015 1.259904 0.001014 1.456160 0.001013 1.302391 0.001012 1.545004 0.001011 1.260239 "Vargas v. Pfizer, Inc. et al., SDNY Cause No. 04-CV-9772 (WHP) - Expert opinion and FFT Analysis"

0.022449 0.022472 0.022494 0.022517 0.022540 0.022562 0.022585 0.022608 0.022630 0.022653 0.022676 0.022698 0.022721 0.022744 0.022766 0.022789 0.022812 0.022834 0.022857 0.022880 0.022902 0.022925 0.022948 0.022971 0.022993 0.023016 0.023039 0.023061 0.023084 0.023107 0.023129 0.023152 0.023175 0.023197

0.001010 0.001009 0.001008 0.001007 0.001006 0.001005 0.001004 0.001003 0.001002 0.001001 0.001000 0.000999 0.000998 0.000997 0.000996 0.000995 0.000994 0.000993 0.000992 0.000991 0.000990 0.000989 0.000988 0.000987 0.000986 0.000985 0.000984 0.000983 0.000982 0.000981 0.000980 0.000979 0.000978 0.000978

0.009849 -0.000000 0.115056 0.270359 0.000000 -0.000000 0.000000 -0.000000 0.000000 0.086462 0.000000 -0.000000 0.000000 -0.000000 0.000000 -0.000000 0.114648 0.426149 0.210781 -0.000000 0.019569 0.781381 1.247215 0.943327 0.784468 0.320760 0.000000 0.000000 0.000000 0.000000 0.000000 -0.000000 0.000000 -0.000000

Fig27. Audacity Enhanced Correlation Frequency Analysis DATA 1-bar Loop (Aparthenonia) Lag (seconds) 0.000023 0.000045 0.000068 0.000091 0.000113 0.000136 0.000159 0.000181 0.000204 0.000227 0.000249 0.000272 0.000295 0.000317 0.000340 0.000363 0.000385 0.000408 0.000431 0.000454 0.000476 0.000499 0.000522 0.000544 0.000567 0.000590 0.000612 0.000635 Boulanger 38: Frequency (Hz) Level 1.000000 0.000000 0.500000 0.000000 0.333333 0.000000 0.250000 0.000000 0.200000 0.000000 0.166667 0.000000 0.142857 0.000000 0.125000 0.000000 0.111111 18.669552 0.100000 49.882973 0.090909 62.977875 0.083333 69.884865 0.076923 58.590759 0.071429 51.701046 0.066667 43.640594 0.062500 33.619461 0.058824 25.040897 0.055556 10.577820 0.052632 0.000000 0.050000 0.000000 0.047619 0.000000 0.045455 0.000000 0.043478 0.000000 0.041667 0.000000 0.040000 0.000000 0.038462 0.000000 0.037037 0.000000 0.035714 0.000000 "Vargas v. Pfizer, Inc. et al., SDNY Cause No. 04-CV-9772 (WHP) - Expert opinion and FFT Analysis"

0.000658 0.000680 0.000703 0.000726 0.000748 0.000771 0.000794 0.000816 0.000839 0.000862 0.000884 0.000907 0.000930 0.000952 0.000975 0.000998 0.001020 0.001043 0.001066 0.001088 0.001111 0.001134 0.001156 0.001179 0.001202 0.001224 0.001247 0.001270 0.001293 0.001315 0.001338 0.001361 0.001383 0.001406 0.001429 0.001451 0.001474 0.001497 0.001519 0.001542 0.001565 0.001587 0.001610 0.001633 0.001655 0.001678 0.001701 0.001723 0.001746 0.001769 0.001791 0.001814 0.001837 0.001859 0.001882 0.001905 0.001927 0.001950 0.001973 0.001995 0.002018 0.002041 0.002063 0.002086 0.002109 0.002132 Boulanger

39:

0.034483 0.000000 0.033333 0.000000 0.032258 0.000000 0.031250 0.000000 0.030303 0.000000 0.029412 0.000000 0.028571 0.000000 0.027778 0.000000 0.027027 0.000000 0.026316 0.000000 0.025641 0.000000 0.025000 0.000000 0.024390 0.000000 0.023810 0.000000 0.023256 0.000000 0.022727 0.000000 0.022222 0.000000 0.021739 0.000000 0.021277 0.000000 0.020833 0.000000 0.020408 0.000000 0.020000 0.000000 0.019608 0.000000 0.019231 0.000000 0.018868 0.000000 0.018519 0.000000 0.018182 0.000000 0.017857 0.000000 0.017544 0.000000 0.017241 0.000000 0.016949 0.000000 0.016667 0.000000 0.016393 0.000000 0.016129 0.000000 0.015873 0.000000 0.015625 0.000000 0.015385 0.000000 0.015152 0.000000 0.014925 0.000000 0.014706 0.000000 0.014493 0.000000 0.014286 0.000000 0.014085 0.000000 0.013889 0.000000 0.013699 0.000000 0.013514 0.000000 0.013333 0.000000 0.013158 0.000000 0.012987 0.000000 0.012821 0.000000 0.012658 0.000000 0.012500 0.000000 0.012346 0.000000 0.012195 0.000000 0.012048 0.000000 0.011905 0.000000 0.011765 0.000000 0.011628 0.000000 0.011494 0.000000 0.011364 0.000000 0.011236 0.000000 0.011111 0.000000 0.010989 0.000000 0.010870 0.000000 0.010753 0.000000 0.010638 0.000000 "Vargas v. Pfizer, Inc. et al., SDNY Cause No. 04-CV-9772 (WHP) - Expert opinion and FFT Analysis"

0.002154 0.002177 0.002200 0.002222 0.002245 0.002268 0.002290 0.002313 0.002336 0.002358 0.002381 0.002404 0.002426 0.002449 0.002472 0.002494 0.002517 0.002540 0.002562 0.002585 0.002608 0.002630 0.002653 0.002676 0.002698 0.002721 0.002744 0.002766 0.002789 0.002812 0.002834 0.002857 0.002880 0.002902 0.002925 0.002948 0.002971 0.002993 0.003016 0.003039 0.003061 0.003084 0.003107 0.003129 0.003152 0.003175 0.003197 0.003220 0.003243 0.003265 0.003288 0.003311 0.003333 0.003356 0.003379 0.003401 0.003424 0.003447 0.003469 0.003492 0.003515 0.003537 0.003560 0.003583 0.003605 0.003628 Boulanger

40:

0.010526 0.000000 0.010417 0.000000 0.010309 0.000000 0.010204 0.000000 0.010101 0.000000 0.010000 0.000000 0.009901 0.000000 0.009804 0.000000 0.009709 0.000000 0.009615 0.000000 0.009524 0.000000 0.009434 0.000000 0.009346 0.000000 0.009259 0.000000 0.009174 0.000000 0.009091 0.000000 0.009009 0.000000 0.008929 0.000000 0.008850 0.000000 0.008772 0.000000 0.008696 0.000000 0.008621 0.000000 0.008547 0.000000 0.008475 0.000000 0.008403 0.000000 0.008333 0.000000 0.008264 0.000000 0.008197 0.000000 0.008130 0.000000 0.008065 0.000000 0.008000 0.000000 0.007937 0.000000 0.007874 0.000000 0.007812 0.000000 0.007752 0.000000 0.007692 0.000000 0.007634 0.000000 0.007576 0.000000 0.007519 0.000000 0.007463 0.000000 0.007407 0.000000 0.007353 0.000000 0.007299 0.000000 0.007246 0.000000 0.007194 0.000000 0.007143 0.000000 0.007092 -0.000000 0.007042 0.000000 0.006993 -0.000000 0.006944 0.000000 0.006897 -0.000000 0.006849 0.000000 0.006803 -0.000000 0.006757 0.000000 0.006711 -0.000000 0.006667 0.000000 0.006623 -0.000000 0.006579 0.000000 0.006536 -0.000000 0.006494 0.000000 0.006452 -0.000000 0.006410 0.000000 0.006369 -0.000000 0.006329 0.000000 0.006289 -0.000000 0.006250 0.000000 "Vargas v. Pfizer, Inc. et al., SDNY Cause No. 04-CV-9772 (WHP) - Expert opinion and FFT Analysis"

0.003651 0.003673 0.003696 0.003719 0.003741 0.003764 0.003787 0.003810 0.003832 0.003855 0.003878 0.003900 0.003923 0.003946 0.003968 0.003991 0.004014 0.004036 0.004059 0.004082 0.004104 0.004127 0.004150 0.004172 0.004195 0.004218 0.004240 0.004263 0.004286 0.004308 0.004331 0.004354 0.004376 0.004399 0.004422 0.004444 0.004467 0.004490 0.004512 0.004535 0.004558 0.004580 0.004603 0.004626 0.004649 0.004671 0.004694 0.004717 0.004739 0.004762 0.004785 0.004807 0.004830 0.004853 0.004875 0.004898 0.004921 0.004943 0.004966 0.004989 0.005011 0.005034 0.005057 0.005079 0.005102 0.005125 Boulanger

41:

0.006211 -0.000000 0.006173 0.000000 0.006135 -0.000000 0.006098 0.000000 0.006061 -0.000000 0.006024 0.000000 0.005988 -0.000000 0.005952 0.000000 0.005917 -0.000000 0.005882 0.000000 0.005848 -0.000000 0.005814 0.000000 0.005780 -0.000000 0.005747 0.000000 0.005714 -0.000000 0.005682 0.000000 0.005650 -0.000000 0.005618 0.000000 0.005587 -0.000000 0.005556 0.000000 0.005525 -0.000000 0.005495 0.000000 0.005464 -0.000000 0.005435 0.000000 0.005405 -0.000000 0.005376 0.000000 0.005348 -0.000000 0.005319 0.000000 0.005291 -0.000000 0.005263 0.000000 0.005236 -0.000000 0.005208 0.000000 0.005181 -0.000000 0.005155 0.000000 0.005128 -0.000000 0.005102 0.000000 0.005076 -0.000000 0.005051 0.000000 0.005025 -0.000000 0.005000 0.000000 0.004975 -0.000000 0.004950 0.000000 0.004926 -0.000000 0.004902 0.000000 0.004878 -0.000000 0.004854 0.000000 0.004831 -0.000000 0.004808 0.000000 0.004785 -0.000000 0.004762 0.000000 0.004739 -0.000000 0.004717 0.000000 0.004695 -0.000000 0.004673 0.000000 0.004651 -0.000000 0.004630 0.000000 0.004608 -0.000000 0.004587 0.000000 0.004566 -0.000000 0.004545 0.000000 0.004525 -0.000000 0.004505 0.000000 0.004484 -0.000000 0.004464 0.000000 0.004444 -0.000000 0.004425 0.000000 "Vargas v. Pfizer, Inc. et al., SDNY Cause No. 04-CV-9772 (WHP) - Expert opinion and FFT Analysis"

0.005147 0.005170 0.005193 0.005215 0.005238 0.005261 0.005283 0.005306 0.005329 0.005351 0.005374 0.005397 0.005420 0.005442 0.005465 0.005488 0.005510 0.005533 0.005556 0.005578 0.005601 0.005624 0.005646 0.005669 0.005692 0.005714 0.005737 0.005760 0.005782 0.005805 0.005828 0.005850 0.005873 0.005896 0.005918 0.005941 0.005964 0.005986 0.006009 0.006032 0.006054 0.006077 0.006100 0.006122 0.006145 0.006168 0.006190 0.006213 0.006236 0.006259 0.006281 0.006304 0.006327 0.006349 0.006372 0.006395 0.006417 0.006440 0.006463 0.006485 0.006508 0.006531 0.006553 0.006576 0.006599 0.006621 Boulanger

42:

0.004405 -0.000000 0.004386 0.000000 0.004367 -0.000000 0.004348 0.000000 0.004329 -0.000000 0.004310 0.000000 0.004292 -0.000000 0.004274 0.000000 0.004255 -0.000000 0.004237 0.000000 0.004219 -0.000000 0.004202 0.000000 0.004184 -0.000000 0.004167 0.000000 0.004149 -0.000000 0.004132 0.000000 0.004115 -0.000000 0.004098 0.000000 0.004082 -0.000000 0.004065 0.000000 0.004049 -0.000000 0.004032 0.000000 0.004016 -0.000000 0.004000 0.000000 0.003984 -0.000000 0.003968 0.000000 0.003953 -0.000000 0.003937 0.000000 0.003922 -0.000000 0.003906 0.000000 0.003891 -0.000000 0.003876 0.000000 0.003861 -0.000000 0.003846 0.000000 0.003831 -0.000000 0.003817 0.000000 0.003802 -0.000000 0.003788 0.000000 0.003774 -0.000000 0.003759 0.000000 0.003745 -0.000000 0.003731 0.000000 0.003717 -0.000000 0.003704 0.000000 0.003690 -0.000000 0.003676 0.000000 0.003663 -0.000000 0.003650 0.000000 0.003636 -0.000000 0.003623 0.000000 0.003610 -0.000000 0.003597 0.000000 0.003584 -0.000000 0.003571 0.000000 0.003559 -0.000000 0.003546 0.000000 0.003534 -0.000000 0.003521 0.000000 0.003509 -0.000000 0.003497 0.000000 0.003484 -0.000000 0.003472 0.000000 0.003460 -0.000000 0.003448 0.000000 0.003436 -0.000000 0.003425 0.000000 "Vargas v. Pfizer, Inc. et al., SDNY Cause No. 04-CV-9772 (WHP) - Expert opinion and FFT Analysis"

0.006644 0.006667 0.006689 0.006712 0.006735 0.006757 0.006780 0.006803 0.006825 0.006848 0.006871 0.006893 0.006916 0.006939 0.006961 0.006984 0.007007 0.007029 0.007052 0.007075 0.007098 0.007120 0.007143 0.007166 0.007188 0.007211 0.007234 0.007256 0.007279 0.007302 0.007324 0.007347 0.007370 0.007392 0.007415 0.007438 0.007460 0.007483 0.007506 0.007528 0.007551 0.007574 0.007596 0.007619 0.007642 0.007664 0.007687 0.007710 0.007732 0.007755 0.007778 0.007800 0.007823 0.007846 0.007868 0.007891 0.007914 0.007937 0.007959 0.007982 0.008005 0.008027 0.008050 0.008073 0.008095 0.008118 Boulanger

43:

0.003413 -0.000000 0.003401 0.000000 0.003390 -0.000000 0.003378 0.000000 0.003367 -0.000000 0.003356 0.000000 0.003344 -0.000000 0.003333 0.000000 0.003322 -0.000000 0.003311 0.000000 0.003300 -0.000000 0.003289 0.000000 0.003279 -0.000000 0.003268 0.000000 0.003257 -0.000000 0.003247 0.000000 0.003236 -0.000000 0.003226 0.000000 0.003215 -0.000000 0.003205 0.000000 0.003195 -0.000000 0.003185 0.000000 0.003175 -0.000000 0.003165 0.000000 0.003155 -0.000000 0.003145 0.000000 0.003135 -0.000000 0.003125 0.000000 0.003115 -0.000000 0.003106 0.000000 0.003096 -0.000000 0.003086 0.000000 0.003077 -0.000000 0.003067 0.000000 0.003058 -0.000000 0.003049 0.000000 0.003040 -0.000000 0.003030 0.000000 0.003021 -0.000000 0.003012 0.000000 0.003003 -0.000000 0.002994 0.000000 0.002985 -0.000000 0.002976 0.000000 0.002967 -0.000000 0.002959 0.000000 0.002950 -0.000000 0.002941 0.000000 0.002933 -0.000000 0.002924 0.000000 0.002915 -0.000000 0.002907 0.000000 0.002899 -0.000000 0.002890 0.000000 0.002882 -0.000000 0.002874 0.000000 0.002865 -0.000000 0.002857 0.000000 0.002849 -0.000000 0.002841 0.000000 0.002833 -0.000000 0.002825 0.000000 0.002817 -0.000000 0.002809 0.000000 0.002801 -0.000000 0.002793 0.000000 "Vargas v. Pfizer, Inc. et al., SDNY Cause No. 04-CV-9772 (WHP) - Expert opinion and FFT Analysis"

0.008141 0.008163 0.008186 0.008209 0.008231 0.008254 0.008277 0.008299 0.008322 0.008345 0.008367 0.008390 0.008413 0.008435 0.008458 0.008481 0.008503 0.008526 0.008549 0.008571 0.008594 0.008617 0.008639 0.008662 0.008685 0.008707 0.008730 0.008753 0.008776 0.008798 0.008821 0.008844 0.008866 0.008889 0.008912 0.008934 0.008957 0.008980 0.009002 0.009025 0.009048 0.009070 0.009093 0.009116 0.009138 0.009161 0.009184 0.009206 0.009229 0.009252 0.009274 0.009297 0.009320 0.009342 0.009365 0.009388 0.009410 0.009433 0.009456 0.009478 0.009501 0.009524 0.009546 0.009569 0.009592 0.009615 Boulanger

44:

0.002786 -0.000000 0.002778 0.000000 0.002770 -0.000000 0.002762 0.000000 0.002755 -0.000000 0.002747 0.000000 0.002740 -0.000000 0.002732 0.000000 0.002725 -0.000000 0.002717 0.000000 0.002710 -0.000000 0.002703 0.000000 0.002695 -0.000000 0.002688 0.000000 0.002681 -0.000000 0.002674 0.000000 0.002667 -0.000000 0.002660 0.000000 0.002653 -0.000000 0.002646 0.000000 0.002639 -0.000000 0.002632 0.000000 0.002625 -0.000000 0.002618 0.000000 0.002611 -0.000000 0.002604 0.000000 0.002597 -0.000000 0.002591 0.000000 0.002584 -0.000000 0.002577 0.000000 0.002571 -0.000000 0.002564 0.000000 0.002558 -0.000000 0.002551 0.000000 0.002545 -0.000000 0.002538 0.000000 0.002532 -0.000000 0.002525 0.000000 0.002519 -0.000000 0.002513 0.000000 0.002506 -0.000000 0.002500 0.000000 0.002494 -0.000000 0.002488 0.000000 0.002481 -0.000000 0.002475 0.000000 0.002469 -0.000000 0.002463 0.000000 0.002457 -0.000000 0.002451 0.000000 0.002445 -0.000000 0.002439 0.000000 0.002433 -0.000000 0.002427 0.000000 0.002421 -0.000000 0.002415 0.000000 0.002410 -0.000000 0.002404 0.000000 0.002398 -0.000000 0.002392 0.000000 0.002387 -0.000000 0.002381 0.000000 0.002375 -0.000000 0.002370 0.000000 0.002364 -0.000000 0.002358 0.000000 "Vargas v. Pfizer, Inc. et al., SDNY Cause No. 04-CV-9772 (WHP) - Expert opinion and FFT Analysis"

0.009637 0.009660 0.009683 0.009705 0.009728 0.009751 0.009773 0.009796 0.009819 0.009841 0.009864 0.009887 0.009909 0.009932 0.009955 0.009977 0.010000 0.010023 0.010045 0.010068 0.010091 0.010113 0.010136 0.010159 0.010181 0.010204 0.010227 0.010249 0.010272 0.010295 0.010317 0.010340 0.010363 0.010385 0.010408 0.010431 0.010454 0.010476 0.010499 0.010522 0.010544 0.010567 0.010590 0.010612 0.010635 0.010658 0.010680 0.010703 0.010726 0.010748 0.010771 0.010794 0.010816 0.010839 0.010862 0.010884 0.010907 0.010930 0.010952 0.010975 0.010998 0.011020 0.011043 0.011066 0.011088 0.011111 Boulanger

45:

0.002353 -0.000000 0.002347 0.000000 0.002342 -0.000000 0.002336 0.000000 0.002331 -0.000000 0.002326 0.000000 0.002320 -0.000000 0.002315 0.000000 0.002309 -0.000000 0.002304 0.000000 0.002299 -0.000000 0.002294 0.000000 0.002288 -0.000000 0.002283 0.000000 0.002278 -0.000000 0.002273 0.000000 0.002268 -0.000000 0.002262 0.000000 0.002257 -0.000000 0.002252 0.000000 0.002247 -0.000000 0.002242 0.000000 0.002237 -0.000000 0.002232 0.000000 0.002227 -0.000000 0.002222 0.000000 0.002217 -0.000000 0.002212 0.000000 0.002208 -0.000000 0.002203 0.000000 0.002198 -0.000000 0.002193 0.000000 0.002188 -0.000000 0.002183 0.000000 0.002179 -0.000000 0.002174 0.000000 0.002169 -0.000000 0.002165 0.000000 0.002160 -0.000000 0.002155 0.000000 0.002151 -0.000000 0.002146 0.000000 0.002141 -0.000000 0.002137 0.000000 0.002132 -0.000000 0.002128 0.000000 0.002123 -0.000000 0.002119 0.000000 0.002114 -0.000000 0.002110 0.000000 0.002105 -0.000000 0.002101 0.000000 0.002096 -0.000000 0.002092 0.000000 0.002088 -0.000000 0.002083 0.000000 0.002079 -0.000000 0.002075 0.000000 0.002070 -0.000000 0.002066 0.000000 0.002062 -0.000000 0.002058 0.000000 0.002053 -0.000000 0.002049 0.000000 0.002045 -0.000000 0.002041 0.000000 "Vargas v. Pfizer, Inc. et al., SDNY Cause No. 04-CV-9772 (WHP) - Expert opinion and FFT Analysis"

0.011134 0.011156 0.011179 0.011202 0.011224 0.011247 0.011270 0.011293 0.011315 0.011338 0.011361 0.011383 0.011406 0.011429 0.011451 0.011474 0.011497 0.011519 0.011542 0.011565 0.011587 0.011610 0.011633 0.011655 0.011678 0.011701 0.011723 0.011746 0.011769 0.011791 0.011814 0.011837 0.011859 0.011882 0.011905 0.011927 0.011950 0.011973 0.011995 0.012018 0.012041 0.012063 0.012086 0.012109 0.012132 0.012154 0.012177 0.012200 0.012222 0.012245 0.012268 0.012290 0.012313 0.012336 0.012358 0.012381 0.012404 0.012426 0.012449 0.012472 0.012494 0.012517 0.012540 0.012562 0.012585 0.012608 Boulanger

46:

0.002037 -0.000000 0.002033 0.000000 0.002028 -0.000000 0.002024 0.000000 0.002020 -0.000000 0.002016 0.000000 0.002012 -0.000000 0.002008 0.000000 0.002004 -0.000000 0.002000 0.000000 0.001996 -0.000000 0.001992 0.000000 0.001988 -0.000000 0.001984 0.000000 0.001980 -0.000000 0.001976 0.000000 0.001972 -0.000000 0.001969 0.000000 0.001965 -0.000000 0.001961 0.000000 0.001957 -0.000000 0.001953 0.000000 0.001949 -0.000000 0.001946 0.000000 0.001942 -0.000000 0.001938 0.000000 0.001934 -0.000000 0.001931 0.000000 0.001927 0.808258 0.001923 0.641052 0.001919 0.892074 0.001916 0.843530 0.001912 0.589923 0.001908 1.221856 0.001905 1.812258 0.001901 2.073065 0.001898 1.794521 0.001894 0.163437 0.001890 -0.000000 0.001887 0.000000 0.001883 -0.000000 0.001880 0.000000 0.001876 -0.000000 0.001873 0.000000 0.001869 0.818218 0.001866 1.101695 0.001862 1.196628 0.001859 1.232234 0.001855 0.712272 0.001852 0.453743 0.001848 0.694763 0.001845 0.668010 0.001842 1.090125 0.001838 1.728920 0.001835 1.970919 0.001832 2.547507 0.001828 3.284037 0.001825 3.554055 0.001821 3.288257 0.001818 2.104790 0.001815 0.905991 0.001812 0.921656 0.001808 1.113813 0.001805 1.346493 0.001802 2.479781 0.001799 3.920736 "Vargas v. Pfizer, Inc. et al., SDNY Cause No. 04-CV-9772 (WHP) - Expert opinion and FFT Analysis"

0.012630 0.012653 0.012676 0.012698 0.012721 0.012744 0.012766 0.012789 0.012812 0.012834 0.012857 0.012880 0.012902 0.012925 0.012948 0.012971 0.012993 0.013016 0.013039 0.013061 0.013084 0.013107 0.013129 0.013152 0.013175 0.013197 0.013220 0.013243 0.013265 0.013288 0.013311 0.013333 0.013356 0.013379 0.013401 0.013424 0.013447 0.013469 0.013492 0.013515 0.013537 0.013560 0.013583 0.013605 0.013628 0.013651 0.013673 0.013696 0.013719 0.013741 0.013764 0.013787 0.013810 0.013832 0.013855 0.013878 0.013900 0.013923 0.013946 0.013968 0.013991 0.014014 0.014036 0.014059 0.014082 0.014104 Boulanger

47:

0.001795 4.347955 0.001792 4.023615 0.001789 3.671635 0.001786 3.517332 0.001783 2.688346 0.001779 2.186292 0.001776 2.877953 0.001773 2.996251 0.001770 2.103060 0.001767 1.160695 0.001764 0.499367 0.001761 0.983003 0.001757 2.233394 0.001754 2.969776 0.001751 3.546423 0.001748 3.884597 0.001745 3.748905 0.001742 3.979084 0.001739 3.627683 0.001736 2.714820 0.001733 2.546650 0.001730 2.532441 0.001727 1.813203 0.001724 1.321680 0.001721 1.647390 0.001718 2.777740 0.001715 3.624499 0.001712 3.254443 0.001709 2.728869 0.001706 2.261204 0.001704 1.098860 0.001701 0.561560 0.001698 0.942437 0.001695 1.284463 0.001692 1.317001 0.001689 0.763905 0.001686 0.039849 0.001684 0.213438 0.001681 0.512577 0.001678 0.084196 0.001675 -0.000000 0.001672 0.756541 0.001669 1.570849 0.001667 1.034311 0.001664 0.166570 0.001661 0.422000 0.001658 0.478493 0.001656 0.196840 0.001653 0.905499 0.001650 1.644683 0.001647 2.048052 0.001645 2.208261 0.001642 2.126045 0.001639 2.679866 0.001637 3.443489 0.001634 3.578214 0.001631 3.534057 0.001629 3.165654 0.001626 2.384752 0.001623 2.491642 0.001621 2.589838 0.001618 2.275225 0.001616 2.441985 0.001613 2.196888 0.001610 1.586583 0.001608 2.125755 "Vargas v. Pfizer, Inc. et al., SDNY Cause No. 04-CV-9772 (WHP) - Expert opinion and FFT Analysis"

0.014127 0.014150 0.014172 0.014195 0.014218 0.014240 0.014263 0.014286 0.014308 0.014331 0.014354 0.014376 0.014399 0.014422 0.014444 0.014467 0.014490 0.014512 0.014535 0.014558 0.014580 0.014603 0.014626 0.014649 0.014671 0.014694 0.014717 0.014739 0.014762 0.014785 0.014807 0.014830 0.014853 0.014875 0.014898 0.014921 0.014943 0.014966 0.014989 0.015011 0.015034 0.015057 0.015079 0.015102 0.015125 0.015147 0.015170 0.015193 0.015215 0.015238 0.015261 0.015283 0.015306 0.015329 0.015351 0.015374 0.015397 0.015420 0.015442 0.015465 0.015488 0.015510 0.015533 0.015556 0.015578 0.015601 Boulanger

48:

0.001605 2.935488 0.001603 3.047837 0.001600 2.773730 0.001597 2.255352 0.001595 2.017529 0.001592 2.095798 0.001590 1.960902 0.001587 2.189210 0.001585 2.431791 0.001582 2.658551 0.001580 3.874837 0.001577 5.247653 0.001575 5.339801 0.001572 5.091010 0.001570 4.866868 0.001567 4.730077 0.001565 4.290058 0.001563 3.744851 0.001560 3.781959 0.001558 4.053973 0.001555 3.532215 0.001553 3.325413 0.001550 3.787084 0.001548 4.419772 0.001546 5.202283 0.001543 5.391574 0.001541 4.839568 0.001538 4.589694 0.001536 4.094831 0.001534 3.645138 0.001531 3.962634 0.001529 3.992508 0.001527 3.289826 0.001524 2.622720 0.001522 2.549607 0.001520 3.114512 0.001517 3.766804 0.001515 4.219452 0.001513 4.830597 0.001511 5.485577 0.001508 5.632105 0.001506 5.611520 0.001504 4.957497 0.001502 4.080578 0.001499 3.738961 0.001497 3.660589 0.001495 3.687729 0.001493 4.012693 0.001490 3.976528 0.001488 3.466408 0.001486 3.192668 0.001484 3.483256 0.001481 3.482003 0.001479 3.122925 0.001477 3.307907 0.001475 3.678283 0.001473 3.490303 0.001471 3.517976 0.001468 3.459229 0.001466 2.501504 0.001464 1.589100 0.001462 1.268119 0.001460 1.198435 0.001458 1.912790 0.001456 2.571959 0.001453 2.365465 "Vargas v. Pfizer, Inc. et al., SDNY Cause No. 04-CV-9772 (WHP) - Expert opinion and FFT Analysis"

0.015624 0.015646 0.015669 0.015692 0.015714 0.015737 0.015760 0.015782 0.015805 0.015828 0.015850 0.015873 0.015896 0.015918 0.015941 0.015964 0.015986 0.016009 0.016032 0.016054 0.016077 0.016100 0.016122 0.016145 0.016168 0.016190 0.016213 0.016236 0.016259 0.016281 0.016304 0.016327 0.016349 0.016372 0.016395 0.016417 0.016440 0.016463 0.016485 0.016508 0.016531 0.016553 0.016576 0.016599 0.016621 0.016644 0.016667 0.016689 0.016712 0.016735 0.016757 0.016780 0.016803 0.016825 0.016848 0.016871 0.016893 0.016916 0.016939 0.016961 0.016984 0.017007 0.017029 0.017052 0.017075 0.017098 Boulanger

49:

0.001451 1.859181 0.001449 1.675969 0.001447 1.911246 0.001445 2.490105 0.001443 2.399604 0.001441 1.935895 0.001439 1.641896 0.001437 1.234890 0.001435 1.096938 0.001433 1.727972 0.001431 1.966495 0.001429 1.695510 0.001427 1.538760 0.0