NASA/TM—2000–209606 # 3-D Sound for Virtual Reality and Multimedia Durand R. Begault Ames Research Center, Moffett Field, California National Aeronautics and Space Administration Ames Research Center Moffett Field, California 94035 ## Acknowledgments Without the assistance and support of Justine, Pat, Denise, Chloe, Nigel, tre, Bill, Lars, Joel, Rick, Dr. B, Jenifer, Reuben, and many others, the completion of this book would not have been possible. ## About the Cover Cylindrical Surface Plot of the Head-Related Transfer Function: Magnitude Response as a Function of Frequency over Azimuth Angle on a Radial Axis, by William Martens of E-mu/Creative Technology Center. The cover photograph shows a visualization of the magnitude response (gain) of the head-related transfer function (HRTF) measured at the eardrum position of the anthropomorphic mannequin KEMAR. HRTFs were measured for 19 loudspeaker directions circling the side of the head facing the loudspeaker placed at ear level. The surface was constructed by interpolating the gain within each of 50 log-spaced frequency bands for the 19 HRTFs using a bicubic spline. The lowest band was centered on 55 Hz, the highest on 21,331 Hz. The distance of the surface from the origin and the color indicates the gain at a particular frequency and azimuth, which ranges from blue-black at the lowest gain (-43.9 dB) to a desaturated yellow at the peak gain (14.6 dB). Available from: National Technical Information Service 5285 Port Royal Road Springfield, VA 22161 703-605-6000 ## Table of Contents Preface to the NASA Technical Memorandum version.....ix Preface.....x Overview.....xii CHAPTER ONE.....1 Virtual Auditory Space: Context, Acoustics, and Psychoacoustics.....1 Context.....1 Source-Medium-Receiver Model: Natural versus Virtual Spatial Hearing.....4 Application Types.....7 Virtual Audio: A Special Case.....11 Components.....12 So What Is 3-D Sound Good For?.....13 Surround versus 3-D Sound.....16 Characteristics of Sound Sources.....17 Describing Waveforms.....17 Periodic and Aperiodic Waveforms.....17 Digital Sound and Signal Processing.....20 Harmonics.....20 Fourier Analysis.....21 Amplitude Envelope.....25 Perception.....25 Psychoacoustics and Applications.....25 Perceptual CorrelatesNASA/TM—2000–209606 # 3-D Sound for Virtual Reality and Multimedia Durand R. Begault Ames Research Center, Moffett Field, California National Aeronautics and Space Administration Ames Research Center Moffett Field, California 94035 ## Acknowledgments Without the assistance and support of Justine, Pat, Denise, Chloe, Nigel, tre, Bill, Lars, Joel, Rick, Dr. B, Jenifer, Reuben, and many others, the completion of this book would not have been possible. ## About the Cover Cylindrical Surface Plot of the Head-Related Transfer Function: Magnitude Response as a Function of Frequency over Azimuth Angle on a Radial Axis, by William Martens of E-mu/Creative Technology Center. The cover photograph shows a visualization of the magnitude response (gain) of the head-related transfer function (HRTF) measured at the eardrum position of the anthropomorphic mannequin KEMAR. HRTFs were measured for 19 loudspeaker directions circling the side of the head facing the loudspeaker placed at ear level. The surface was constructed by interpolating the gain within each of 50 log-spaced frequency bands for the 19 HRTFs using a bicubic spline. The lowest band was centered on 55 Hz, the highest on 21,331 Hz. The distance of the surface from the origin and the color indicates the gain at a particular frequency and azimuth, which ranges from blue-black at the lowest gain (-43.9 dB) to a desaturated yellow at the peak gain (14.6 dB). Available from: National Technical Information Service 5285 Port Royal Road Springfield, VA 22161 703-605-6000 ## Table of Contents Preface to the NASA Technical Memorandum version.....ix Preface.....x Overview.....xii CHAPTER ONE.....1 Virtual Auditory Space: Context, Acoustics, and Psychoacoustics.....1 Context.....1 Source-Medium-Receiver Model: Natural versus Virtual Spatial Hearing.....4 Application Types.....7 Virtual Audio: A Special Case.....11 Components.....12 So What Is 3-D Sound Good For?.....13 Surround versus 3-D Sound.....16 Characteristics of Sound Sources.....17 Describing Waveforms.....17 Periodic and Aperiodic Waveforms.....17 Digital Sound and Signal Processing.....20 Harmonics.....20 Fourier Analysis.....21 Amplitude Envelope.....25 Perception.....25 Psychoacoustics and Applications.....25 Perceptual Correlates