Spatial Soundfield Reproduction Methods Based On Spherical Harmonic Analysis

Three-dimensional audio technology is a focused topic in the area of audio signal processing,and has a wide market foreground.Spatial soundfield reproduction plays a vital role in three-dimensional audio technology.It aims at physically reproducing a desired soundfield over a specific listening area and resulting in an immersive acoustic environment for listeners.Ambisonics is known as one of the most classic three-dimensional audio technologies for reproducing a spatial soundfield,which is based on spherical harmonic decomposition or reconstruction of the soundfield.According to the order of spherical harmonics,Ambisonics system can reproduce the desired soundfield using different numbers of loudspeaker,featuring flexibility and scalability properties.However,in terms of practical applications,there are several critical problems for the existing Ambisonics techniques:?i?The traditional loudspeaker arrays are incompatible with the Ambisonics recorded signals.?ii?The deployment of microphones/loudspeakers must conform to the structure of regular spherical arrays.?iii?Soudfield reproduction suffers from reflection interference in reverberant rooms.To address these critical problems mentioned ealier,on the basis of spherical harmonic analysis,the research works of this dissertation mainly focus on interior and exterior soundfield reproduction using an irregular loudspeaker array,conversion of multichannel sound signals,room transfer function?RTF?measurement and modeling,and room acoustic simulation.The main contributions are given by the following five aspects.1.The design of ambisonic reproduction system based on dynamic gain parametersConventional approaches use the fixed gain parameters to address the incompatible problem between the the existing loudspeaker arrays and the Ambisonics recorded signals.However,the fixed gain parameters bear a mutual contradiction between different angles and get an average localization performance for the whole 360°surround.To overcome the tradeoff among different angles,a design approach of ambisonic reproduction system based on dynamic gain parameters?DGP?is proposed in this dissertation.Based on Gerzon's localization theory,the advantage of DGP is that the objective function is able to attain optimal value for each audible angle.In the training stage,a set of DGP is obtained by minimizing objective function for each audible angle.In the rendering stage,the directions of the B-Format signals are estimated in frequency bands in order to match the corresponding gain parameters.Then,the corresponding gain parameters are applied to reconstruct the soundfields.For the synthesized signals,the process is simplified by the given spatial information.Using binaural cues analysis,the proposed approach is significantly better than reference approaches on the interaural time difference?ITD?and the interaural level difference?ILD?.2.Conversion of multichannel sound signals based on spherical harmonicsIn order to address the conversion of multichannel sound systems,a novel method for converting multichannel signals of an original system into that of an alternative system is proposed in this dissertation.Based on spherical harmonic expansion,we present a conversion formulation to derive the matching equation that explains a direct relationship between weighting matrix and positions of loudspeakers located on both systems.The solution of matching equation can be found from matrix inverse where under-determined problem might exist.To solve this problem,l₁-norm minimization is used for finding constraining the minimum number of the active loudspeakers.Simulations confirm that the proposed method is able to reconstruct original sound field within a finite region of listening and has better performance than traditional method.3.Design of a planar first-order loudspeaker array for exterior soundfield reproductionIn order to change the structure of regular spherical arrays for Ambisonics systems,a method to design a planar first-order loudspeaker array structure for exterior soundfield reproduction is proposed in this dissertation.Compared with the traditional spherical loudspeaker array,the planar array provides a practical design with flexible source locations.On x-y plane,we use spherical harmonics to analyze the general first-order loudspeakers consisting of monopole and tangential dipole components.By exploiting the properties of the associated Legendre functions and its derivative,we can divide the primary soundfield into even harmonics controlled by the monopole component and odd harmonics controlled by the dipole component.Through the appropriate choice of radii of circles,we avoid the ill-conditioning problem of matrix inversion and derive a robust solution for loudspeaker weights.Besides,we use the closely-located monopole pairs,instead of the ideal general first-order loudspeakers,to design an alternative planar array for practical implementation.As an illustration,we use several simulation examples to validate the performance of the two proposed planar loudspeaker arrays.4.Parameterization of the three-dimensional room transfer function in horizontal planeIn order to address the problem of reverberation interference,an efficient parameterization of the three-dimensional room transfer function is proposed,which is robust for the position variations of source and receiver in respective horizontal planes.Based on azimuth harmonic analysis,the proposed method exploits the underlying properties of the associated Legendre functions to remove a portion of the spherical harmonic coefficients of RTF that do not have contribution in the horizontal plane.This reduction leads to a flexible measuring-point structure consisting of practical concentric circular arrays to extract horizontal plane RTF coefficients.The accuracy of the above parameterization is verified through numerical simulations.5.Simulating the three-dimensional room transfer function for a rotatable complex sourceDue to the fact that the traditional room acoustic models are not suitable for directional sound sources,an extended image-source model is proposed to simulate the room transfer function for a rotatable complex source in a three-dimensional reverberant room.Since complex sources radiate soundfields unequally in all directions,the extended ISM needs to consider two issues:the mirroring of source directional patterns and rotation movement of sources.The proposed model uses spherical harmonic decomposition to describe the exterior sound field from the complex source.Based on''axis flip''concept,the mirroring relations between the source and images are summarized by a unified mirroring operator that occurs on the soundfield coefficients.The rotation movement of the source is taken into account by exploiting the rotation property of spherical harmonics.The accuracy of the proposed model is verified through the appropriate simulation examples.