摘要翻译：
球谐矩阵(SHM)广泛应用于离散有限阶正交声场表示，本文主要研究它的条件化问题。SHM已广泛应用于音频领域，如使用扬声器的空间声音再现、头部相关传递函数的正交表示等。SHM的调理性能取决于在三维空间中选择的采样位置。在连续的三维空间中识别最优采样点是一项极具挑战性的任务，它可以为任意数量的采样点提供良好的SHM条件。在本工作中，尝试使用基于优化的技术来解决上述问题的一个离散版本。离散问题是，从三维空间密集采样位置的离散集合中识别最优采样点，使SHM的条件数最小。该方法随后被用于空间声音再现中扬声器几何形状的识别，以及HRTF测量的空间采样配置的选择。应用程序的特定要求被制定为优化问题的附加约束。最近发展起来的混合整数优化求解器已被用于求解公式化问题。所获得的采样位置在每个应用中的性能与现有配置进行了比较。利用条件数、D-测度和光谱失真等客观测度研究了所提出的和现有方法产生的采样配置的性能。观察到所提出的解决方案能够找到采样点，从而得到一个更好的条件SHM，也保持了所有应用特定的要求。
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英文标题：
《On the Conditioning of the Spherical Harmonic Matrix for Spatial Audio
  Applications》
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作者：
C Sandeep Reddy, and Rajesh M Hegde
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最新提交年份：
2018
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分类信息：

一级分类：Electrical Engineering and Systems Science        电气工程与系统科学
二级分类：Audio and Speech Processing        音频和语音处理
分类描述：Theory and methods for processing signals representing audio, speech, and language, and their applications. This includes analysis, synthesis, enhancement, transformation, classification and interpretation of such signals as well as the design, development, and evaluation of associated signal processing systems. Machine learning and pattern analysis applied to any of the above areas is also welcome.  Specific topics of interest include: auditory modeling and hearing aids; acoustic beamforming and source localization; classification of acoustic scenes; speaker separation; active noise control and echo cancellation; enhancement; de-reverberation; bioacoustics; music signals analysis, synthesis and modification; music information retrieval;  audio for multimedia and joint audio-video processing; spoken and written language modeling, segmentation, tagging, parsing, understanding, and translation; text mining; speech production, perception, and psychoacoustics; speech analysis, synthesis, and perceptual modeling and coding; robust speech recognition; speaker recognition and characterization; deep learning, online learning, and graphical models applied to speech, audio, and language signals; and implementation aspects ranging from system architecture to fast algorithms.
处理代表音频、语音和语言的信号的理论和方法及其应用。这包括分析、合成、增强、转换、分类和解释这些信号，以及相关信号处理系统的设计、开发和评估。机器学习和模式分析应用于上述任何领域也是受欢迎的。感兴趣的具体主题包括：听觉建模和助听器；声波束形成与声源定位；声场景分类；说话人分离；有源噪声控制和回声消除；增强；去混响；生物声学；音乐信号的分析、合成与修饰；音乐信息检索；多媒体音频和联合音视频处理；口语和书面语建模、切分、标注、句法分析、理解和翻译；文本挖掘；言语产生、感知和心理声学；语音分析、合成、感知建模和编码；鲁棒语音识别；说话人识别与特征描述；应用于语音、音频和语言信号的深度学习、在线学习和图形模型；以及从系统架构到快速算法的实现方面。
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英文摘要：
  In this paper, we attempt to study the conditioning of the Spherical Harmonic Matrix (SHM), which is widely used in the discrete, limited order orthogonal representation of sound fields. SHM's has been widely used in the audio applications like spatial sound reproduction using loudspeakers, orthogonal representation of Head Related Transfer Functions (HRTFs) etc. The conditioning behaviour of the SHM depends on the sampling positions chosen in the 3D space. Identification of the optimal sampling points in the continuous 3D space that results in a well-conditioned SHM for any number of sampling points is a highly challenging task. In this work, an attempt has been made to solve a discrete version of the above problem using optimization based techniques. The discrete problem is, to identify the optimal sampling points from a discrete set of densely sampled positions of the 3D space, that minimizes the condition number of SHM. This method has been subsequently utilized for identifying the geometry of loudspeakers in the spatial sound reproduction, and in the selection of spatial sampling configurations for HRTF measurement. The application specific requirements have been formulated as additional constraints of the optimization problem. Recently developed mixed-integer optimization solvers have been used in solving the formulated problem. The performance of the obtained sampling position in each application is compared with the existing configurations. Objective measures like condition number, D-measure, and spectral distortion are used to study the performance of the sampling configurations resulting from the proposed and the existing methods. It is observed that the proposed solution is able to find the sampling points that results in a better conditioned SHM and also maintains all the application specific requirements.
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PDF链接：
https://arxiv.org/pdf/1710.08633