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Modeling of the Head-Related Transfer Functions for Reduced Computation and Storage Charles Duncan Lueck Iowa State University

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Modeling of the Head-Related Transfer Functions for Reduced Computation and Storage Charles Duncan Lueck Iowa State University Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 1995 Modeling of the head-related transfer functions for reduced computation and storage Charles Duncan Lueck Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Electrical and Electronics Commons Recommended Citation Lueck, Charles Duncan, "Modeling of the head-related transfer functions for reduced computation and storage " (1995). Retrospective Theses and Dissertations. 10929. https://lib.dr.iastate.edu/rtd/10929 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. INFORMATION TO USERS This mamiscr^t has been reproduced fFom the microfilin master. UMI films the text directly from the origmal or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from ai^ type of con^ter printer. Hie qnallQr of this repfodnction is dqiendent opon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, prim bleedthroug^ substandard marginc^ and in^^rqper alignment can adverse^ affect rq)roduction. 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 copyri^t material had to be removed, a note will indicate the deletion. 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Ml 48106-1346 USA 313.'761-4700 800/521-0600 Modeling of the head-related transfer functions for reduced computation and storage by Charles Duncan Lueck A Dissertation Submitted to the Graduate Faculty in Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY Department; Electrical and Computer Engineering Major: Electrical Engineering (Communications and Signal Processing) Signature was redacted for privacy. Signature was redacted for privacy. Signature was redacted for privacy. For Ae MajofDepStment Signature was redacted for privacy. For the Graduate College Iowa State University Ames, Iowa 1995 Copyright © Charles Duncan Lueck, 1995. All rights reserved. DHI Number: 9531765 Copyright 1995 by Lueck, Charles Duncan All eights reserved. DHI Microform 9531765 Copyright 1995, by OKI Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. UMI 300 North Zeeb Road Ann Arbor, MI 48103 TABLE OF CONTENTS 1. INTRODUCTION 1 1.1 Applications 2 1.2 Objectives 4 1.3 Summary 5 2. SOUND LOCALIZATION THEORY 11 2.1 Background 13 2.2 Measurement of the Head-Related Transfer Functions 16 2.3 Synthesis of Localized Sound 18 2.4 Performance and Implementation Concerns 20 3. INTRODUCTION TO SYSTEM MODELING 22 3.1 System Modeling Problem 22 3.2 Parameter Estimation 25 3.2.1 Direct modeling 25 3.2.2 Indirect modeling 26 3.2.2.1 Least-squares (LS) method 28 3.2.2.2 Modified Prony's metiiod 31 3.2.2.3 Iterative prefiltering method 34 3.2.3 Balanced model reduction 38 iii 3.3 Order Estimation 43 4. MODELING OF THE HEAD-RELATED TRANSFER FUNCTIONS 50 4.1 Minimum-Phase Approximation 50 4.2 Model Order Estimation 55 4.2.1 Application of minimum eigenvalue order estimation to HRTFs 55 4.2.2 The diffuse field and directional transfer functions (DTFs) 58 4.2.3 Application of minimum eigenvalue order estimation to DTFs 60 4.3 Perceptual Enhancement 63 4.3.1 Least-squares method 63 4.3.2 The hearing process and psychoacoustics 63 4.3.3 Critical band smoothing 66 4.3.4 Critical band distance measurement 71 4.3.5 Weighted least-squares error method 71 4.3.6 Iterative prefiltering method 76 4.3.7 Weighted iterative prefiltering method 77 4.3.8 Pole-zero cancellation method 80 4.3.9 Balanced model reduction method 84 4.4 Interpolation 87 5. RESULTS 91 5.1 Critical Band Distance Measurements 92 5.1.1 Effect of smoothing 92 iv 5.1.2 Comparison of modeling techniques 96 5.2 Computation 101 5.3 Localization Tests 107 5.3.1 Objective 107 5.3.2 Synthesis 107 5.3.3 Procedure 108 5.3.4 Analysis 109 6. CONCLUSIONS 119 6.1 Discussion 119 6.2 Future Work 122 ACKNOWLEDGMENTS 124 BIBLIOGRAPHY 125 APPENDIX A 129 APPENDIX B 136 APPENDIX C 145 1 1. INTRODUCTION Recent advances in audio and video processing have accelerated the emergence and development of the three-dimensional virtual display. The main objective of the virtual display is to present aural and visual information in such a manner that it is realistically perceived by the user. Hence, the term "virtual reality" has become a popular buzzword used to describe the technology. Still in its infancy, the virtual display shows signs of great potential, opening the door to a host of innovative applications in areas ranging from control systems to education to entertainment However, the technology required to fully achieve this potential has not yet been realized, and will not be realized without significant additional research. The research presented in this dissertation will be directed toward the implementation of the virtual acoustic display, a device for the synthesis of three-dimensional sound via headphones. The virtual acoustic display typically involves the implementation of digital filters which emulate the head-related transfer functions (HRTFs) [1-3]. These functions represent the transformation of sound pressure from a sound source in free space to the eardrums of the listener. Current implementations generally rely on FIR filtering techniques which result in high computation and storage demands, particularly for real-time systems [2]. Because these demands directiy translate into increased cost of implementation, reduction of computation and storage requirements is of great concem. 2 1.1 Applications Thiee-dimensional audio technology has generally not received the attention of its three-dimensional visual counterpart However, this is also an area of great importance and intensive research. Scientists and engineers have been working to understand the complex physical and psychological principles involved in human sound localization and to apply this understanding toward the development of a virtual acoustic display for conveying three- dimensional sound through headphones. Such an acoustic display would prove beneficial to a wide variety of applications. Among these might be: • Entertainment/Recording [4,5]. Undoubtedly, virtual acoustics will find its way into entertainment applications, both at the consumer level and commercially. Potential exists for the enhancement of movies, musical recordings, video games, and other multimedia applications. True three-dimensional acoustic reproduction would create a level of realism unmatched by today's audio reproduction techniques. • Tool for Scientific Research [2,3]. Headphone-delivered stimulus allows researchers precise control over the sound pressure at the eardrums of the listener. The ability to provide simulated signals equivalent to those heard in a realistic environment is unquestionably a valuable scientific tool in the study of the physical and psychological aspects of sound localization. • Aircraft control and communications [1,4,6]. Aviation applications would particularly benefit from the incorporation of three-dimensional acoustic displays. In air traMc control and collision-avoidance systems, where the operator's spatial awareness is critically 3 impoitant, thiee-dimensional acoustic cues would likely increase efficiency and quicken response times. In the cockpit, localized acoustic cues would instantly convey to the pilot information regarding the proximity and location of other aircraft, obstacles, and targets. • Teleconferencing/Telecoininunieations [S]. The effectiveness of remote communication could certainly be enhanced by the application of three-dimensional acoustics. By providing directional cues to speech, individuals would have the perception of being in the same room as other participants, when, in fact, they might actually be separated geographically by large distances. • Guidance systems for the blind [4]. Another application which has been proposed is the incorporation of a virtual acoustic display as a guidance system for the blind. In this system, the global positioning system (GPS) would be used to provide location information to the system. The guidance system would then provide audible cues indicating one's position in relation to landmarks, to the location of buildings, or to the proximity of a busy street or intersection. In general, three-dimensional acoustic displays would be valuable in any situation in which one's spatial awareness is important, or in any situation in which the added dimension of localized
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