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INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand corner and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the back of the book. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6" x 9" black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order. University Microfilms International A Bell & Howell Information C om pany 300 North Zeeb Road. Ann Arbor. Ml 48106-1346 USA 313/ 761-4700 800/521-0600 Order Number 9219044 Application of Hartley and Hilbert transforms in Fourier transform ion cyclotron resonance mass spectrometry Williams, Christopher Paul, Ph.D. The Ohio State University, 1992 UMI 300 N. Zeeb Rd. Ann Arbor, MI 48106 Application of Hartley and Hilbert Transforms in Fourier Transform Ion Cyclotron Resonance Mass Spectrometry DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Christopher Paul Williams, B.S., M.S. * * * * * The Ohio State University 1992 Dissertation Committee: Approved by Professor A. G. M arshall Professor E. J. Behrman Q h t . f k J M Professor R. T. Ross Adviser Professor G. S. Serif Department of Biochemistry DEDICATION I dedicate this work to my wonderful wife Holly, whose encouragement and support has kept me going throughout my graduate work. Not many women would have shown the same patience and good humor as she did when "a couple of years to finish my degree before we have kids" turned into five years and three children. ii ACKNOWLEDGMENTS I must first express my thanks to Professor Alan Marshall for his guidance, insight, and assistance. I also wish to thank Professor E. J. Behrman for his help earlier in my graduate studies, and for his encouraging me to temporarily leave the business world and come back to finish my doctoral work. I thank all the members of Dr. Marshall's research group for their friendship and assistance over the years. In particular, Dr. Francis Verdun helped me considerably in understanding many of the finer points of the Fourier transform. I also thank Kaye Craggs, Dr. Tom Ricca, and Dr. Charles Cottrell for their help when I needed it. I also w ant to th an k my kids, Bethany (4) and M atthew (2), who have made my stint as a graduate student so much more enjoyable. Without their constant attention and affection my graduate studies could not have lasted nearly so long. I also thank my Mom and Dad for their support throughout my educational career. Finally, I must remember the one who truly deserves the credit for anything that I may may accomplish in life. "Great is the Lord and most worthy of praise; his greatness no one can fathom." "Not to us, O Lord, but to your name be the glory". Psalms 145:3; 115:1. iii VITA October 5, 1958 Bom - Akron, Ohio 1980 B.S., Summa cum laude. Biochemistry, The Ohio State University 1980-1981 National Science Foundation Fellow, The Ohio State University 1982 M.S., Biochemistry, The Ohio State University 1982-1984 Assistant Editor, Chemical Abstracts Service, Columbus, Ohio 1984-1986 Computer Programmer-Analyst, Chemical Abstracts Service, Columbus, Ohio 1986-1987 Ohio State University Fellow, The Ohio State University 1987-1990 Graduate Research Associate, The Ohio State University PUBLICATIONS Williams, ( '. P.; Marshall, A. G. "Hartley Transform Ion Cyclotron Resonance Mass Spectrometry", Analytical Chemistry, 1989, 61, 428- 431. FIELDS OF STUDY Major Field: Biochemistry TABLE OF CONTENTS DEDICATION............................................................................................................ 11 ACKNOWLEDGMENTS......................................................................................... Hi VITA .............................................................................. iv LIST OF TABLES........................................................................................ .7 . ..........................................viii LIST OF FIGURES ................................................................................................... x CHAPTER PAGE I. INTRODUCTION....................................................................................... 1 II. PRINCIPLES AND FEATURES OF FOURIER TRANSFORM ION CYCLOTRON RESONANCE MASS SPECTROMETRY ..................3 Magnetic Sector Mass Spectrometry ...............................................3 Ion Cyclotron Resonance Spectroscopy .........................................4 Basics of Fourier Transform Ion Cyclotron Resonance Mass Spectrometry ................................................................................... 9 Ionization Methods ............................................................................ 17 Excitation Techniques .......................................................................25 Cell Design and Ion Trapping .........................................................28 Data Manipulation .............................................................................34 Current Usage.................................................................................... 36 R eferences ............................................................................................39 III. BIOCHEMICAL APPLICATIONS OF FOURIER TRANSFORM ION CYCLOTRON RESONANCE MASS SPECTROMETRY.................48 Special Concerns ............................................................................... 48 Carbohydrates .................................................................................... 49 P roteins .................................................................................................53 Matrix-Assisted Laser Desorption of Proteins ......................55 Electrospray of Proteins .............................................................57 v Other Biochemical Applications ....................................................60 References ............................................................................................63 IV. APPLICATION OF THE HARTLEY TRANSFORM TO FT/ICR DATA........................................................................................................ 69 Introduction ........................................................................................69 The Fourier Transform ...............................................................69 Phase Shift and Phase Correction ...........................................76 Discrete Nature of Experimental D ata .................................. 79 The Hartley Transform ..................................................................... 92 Experimental .......................................................................................99 Results and Discussion .................................................................. 100 Computer Implementation .......................................................100 Spectral Display Modes ............................................................104 Computational Speed Comparisons ..................................... 104 Precision of the FHT .................................................................. 108 C onclusion .........................................................................................114 R eferences ..........................................................................................115 Appendix .........................................................................................117 V. A FASTER ALGORITHM FOR THE HILBERT TRANSFORM... 145 Mathematical basis of the Hilbert Transform .......................... 145 A New Hilbert Algorithm .............................................................. 146 Experimental .....................................................................................148 Results and Discussion .................................................................. 150 Computation of the Hilbert Transform ................................ 150 Precision of the Hilbert Transform Algorithm ....................150 C onclusion .........................................................................................153 R eferences ..........................................................................................157 Appendix .........................................................................................159 VI. THE HILBERT-TRANSFORMED DISPERSION SPECTRUM AND THE "ENHANCED" ABSORPTION SPECTRUM .........................161 Introduction ......................................................................................

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