Analysis, modeling and wide-area spatiotemporal control of low-frequency sound reproduction Item Type Thesis Authors Hill, Adam J. Citation Thesis (Ph.D.), School of Computer Science and Electronic Engineering -- University of Essex, 2012 Publisher University of Essex Download date 04/10/2021 11:10:16 Link to Item http://hdl.handle.net/10545/230034 Analysis, Modeling and Wide-Area Spatiotemporal Control of Low-Frequency Sound Reproduction Adam J. Hill A thesis submitted for the degree of Doctor of Philosophy School of Computer Science & Electronic Engineering University of Essex January 2012 Low-frequency sound reproduction Summary Summary This research aims to develop a low-frequency response control methodology capable of delivering a consistent spectral and temporal response over a wide listening area. Low- frequency room acoustics are naturally plagued by room-modes, a result of standing waves at frequencies with wavelengths that are integer multiples of one or more room dimension. The standing wave pattern is different for each modal frequency, causing a complicated sound field exhibiting a highly position-dependent frequency response. Enhanced systems are investigated with multiple degrees of freedom (independently- controllable sound radiating sources) to provide adequate low-frequency response control. The proposed solution, termed a chameleon subwoofer array or CSA, adopts the most advantageous aspects of existing room-mode correction methodologies while emphasizing efficiency and practicality. Multiple degrees of freedom are ideally achieved by employing what is designated a hybrid subwoofer, which provides four orthogonal degrees of freedom configured within a modest- sized enclosure. The CSA software algorithm integrates both objective and subjective measures to address listener preferences including the possibility of individual real-time control. CSAs and existing techniques are evaluated within a novel acoustical modeling system (FDTD simulation toolbox) developed to meet the requirements of this research. Extensive virtual development of CSAs has led to experimentation using a prototype hybrid subwoofer. The resulting performance is in line with the simulations, whereby variance across a wide listening area is reduced by over 50% with only four degrees of freedom. A supplemental novel correction algorithm addresses correction issues at select narrow frequency bands. These frequencies are filtered from the signal and replaced using virtual bass to maintain all aural information, a psychoacoustical effect giving the impression of low- frequency. Virtual bass is synthesized using an original hybrid approach combining two mainstream synthesis procedures while suppressing each method‟s inherent weaknesses. This algorithm is demonstrated to improve CSA output efficiency while maintaining acceptable subjective performance. 1 Low-frequency sound reproduction Table of contents Table of contents SUMMARY ......................................................................................................................................... 1 ACKNOWLEDGEMENTS ................................................................................................................ 6 1 INTRODUCTION ..................................................................................................................... 7 1.1 Problem statement ......................................................................................................................... 7 1.2 Proposed solution ........................................................................................................................... 8 1.3 Thesis organization ......................................................................................................................... 8 1.4 Claims for originality ..................................................................................................................... 10 2 LOW-FREQUENCY ROOM ACOUSTICS ........................................................................... 12 2.1 Overview ...................................................................................................................................... 12 2.2 Room-modes ................................................................................................................................ 15 2.2.1 Definition of the low-frequency spectral range ................................................................................. 16 2.2.2 Theoretical modal contributions ........................................................................................................ 17 2.2.3 Spatial variance .................................................................................................................................. 18 2.2.4 Magnitude deviation .......................................................................................................................... 19 2.2.5 Mean output level .............................................................................................................................. 19 2.3 Influential factors ......................................................................................................................... 20 2.3.1 Surface absorption and reactance ..................................................................................................... 20 2.3.2 The Waterhouse effect ....................................................................................................................... 20 2.3.3 Helmholtz resonance .......................................................................................................................... 21 2.3.4 Temperature and humidity ................................................................................................................ 21 2.4 Measurement techniques ............................................................................................................. 22 2.4.1 Maximum length sequences (MLS) .................................................................................................... 22 2.4.2 Tone bursts ......................................................................................................................................... 25 2.5 Chapter summary ......................................................................................................................... 26 3 LOW-FREQUENCY MODELING ......................................................................................... 27 3.1 Simulation methods ...................................................................................................................... 27 3.1.1 Image source ...................................................................................................................................... 27 3.1.2 Ray tracing .......................................................................................................................................... 28 3.1.3 Finite element method (FEM) and boundary element method (BEM) .............................................. 29 3.1.4 Hybrid methods .................................................................................................................................. 30 3.2 Finite-difference time-domain theory ........................................................................................... 30 3.2.1 Structure ............................................................................................................................................. 30 3.2.2 Boundary conditions .......................................................................................................................... 32 3.2.3 Advanced boundary conditions .......................................................................................................... 33 3.2.4 Stability ............................................................................................................................................... 33 3.2.5 Non-rectangular FDTD simulation ...................................................................................................... 34 3.2.6 Non-rectangular and room obstacle grid masking ............................................................................. 36 3.3 Simulation toolbox overview ........................................................................................................ 39 3.3.1 Core simulation code .......................................................................................................................... 39 3.3.2 MATLAB graphical user interface (GUI) programming ....................................................................... 40 3.4 Simulation validation .................................................................................................................... 42 3.4.1 Theoretical modes .............................................................................................................................. 42 3.4.2 Lab measurements ............................................................................................................................. 44 2 Low-frequency sound reproduction Table of contents 3.4.3 Previously published results ............................................................................................................... 45 3.4.4 Discussion ........................................................................................................................................... 47 3.5 Chapter summary ........................................................................................................................