超球空间中广义角动量波函数

利用复变函数及高级超越函数的性质,得到了多维超球空间中广义解动量波函数的完备集,给出了多维超球空广义角动量的本征值,多维空间中平面波展开关系式及其它关系式。     

圆柱腔低频声场的球谐函数分解及声场再现

针对圆柱腔低频声场的球谐函数分解,提出了基于移动式球形传声器阵列(简称球阵)测量的空间域直接求解法。利用空间域测量数据,在压缩感知(Compressive Sensing,CS)理论框架下通过一次线性方程组求解,获得整体坐标系下的声场展开系数。首先讨论了感知矩阵的列相关性,比较不同球阵形式及球面采样点数目,不同球谐函数截断阶数以及空间测量位置等的影响。随后在飞机舱室模型内利用文中提出的方法求解声场展开系数,再现腔内水平面的声压分布,并与传统球坐标变换方法做比较。实验结果表明,利用空间域直接求解法,通过球面随机挑选10个采样点的刚性球阵在声腔3个位置进行声场测量,不仅能够有效求解声场展开系数,而且声场再现精度更高,同时计算效率也显著提高。      

粗糙目标样片光谱双向反射分布函数的实验测量及其建模

实验测量了紫红色和白色涂漆板在400～780 nm内的光谱双向反射分布函数(光谱BRDF),分析了光谱双向反射分布函数随波长及散射角的变化趋势与目标样片光学特性的关系.应用改进的粒子群算法,结合双向反射分布函数五参量模型,获得了测量光谱范围内各波长(间隔1 nm)对应的共381组五参量值.利用五参量模型计算了目标样片的光谱双向反射分布函数及其方向半球反射率(DHR),并与实验测量数据相比较,两者吻合良好,表明目标光谱双向反射分布函数建模方法与结果的可行性和可靠性.目标样片的光谱双向反射分布函数可以用来研究目标的光谱散射特性,对目标的探测、跟踪、识别和特征提取等具有重要的应用价值.     

基于空间特征抽取与神经网络的人耳空间听觉模型

空间听觉中复数值的与头相关联的传递函数（ＨＲＴＦ）可用实数值的与头相关联的冲激响应（ＨＲＩＲ表示。对测量空间上归一化的ＨＲＩＲ进行Ｋａｒｈｕｎｅｎ－Ｌｏｅｖｅ展开可以提取其空间特征．用Ｖｏｎ—Ｍｉｓｅｓ函数为基函数的神经网络逼近离散的ＨＲＩＲ空间特征函数得到连续听觉空间上的双耳时域模型．模型与实际测量得到的ＨＲＩＲ有较好的一致性。     

头相关传输函数空间对称性的分析

提出了分析头相关传输函数空间对称性的方法。利用对KEMAR人工头/躯干系统和真人受试者进行测量得到的头相关传输函数,分析了生理结构对头相关传输函数空间对称性的影响。结果表明,在5 kHz至6 kHz以上的频率,耳廓破坏了头相关传输函数的前后对称性；而受耳道入口位置的影响,真人受试者的头相关传输函数在2．5 kHz以上的频率就开始出现前后不对称。另一方面,在中、低频的情况下,头相关传输函数近似左右对称,然而随着频率的升高,生理外形在细微结构上的左右差异将导致头相关传输函数的左右不对称。这种左右不对称的起始频率和程度存在个体差异。上述分析可以反映出头相关传输函数空间对称性的规律和现有双耳听觉模型的适用范围。     

空间太阳望远镜偏振光测量技术

在空间天文望远镜上,由于需要用科学仪器采集太阳偏振图像,所以引出了对偏振光测量问题的研究。利用Stockes参数进行偏振光测量,可以使得原本需要对两个方向的振幅(a1,a2)和相位差进行测量的问题转化为对三个都是强度量纲的Stockes参数进行测量,这就使得测量和实现起来变得简单和容易多了。利用Stockes参数讨论了偏振光测量的原理和方法,并描述了它在空间天文望远镜(SST)中的实现方案。     

超球坐标下Li原子基态能量的快速收敛计算

将Ｌｉ原子２Ｓ态的波函数分解为两项之积，ψ＝ＸΦ，Ｘ＝ｅｘｐ［－α（ｒ１＋ｒ２＋ｒ３）］，而Φ向以九维超球谐为投影函数而构造的Ｓ３置换群的二维不可约表示的基函数展开。Ｓｃｈｒｏｄｉｎｇｅｒ方程转化为一起球径耦合微分方程。再利用广义Ｌａｇｕｅｒｒｅ函数展开法对其求解，从而得到一广义能量本征方程，给出了库仑势及有关超球角函数在非对称九维超球谐之间矩阵元的简单解析式，可由一起几何函数４Ｆ３：（Ａ，Ｂ，Ｃ，Ｄ；Ｅ，Ｆ，Ｇ；１）的线性组合表示。取超球谐函数的子集（ｌ１＝ｌ２＝ｌ３＝０），基态１２Ｓ的本征能量在超球角方向的收敛速度加快，首次用非变分法得到了优于Ｈａｒｔｒｅｅ－Ｆｏｃｋ精度的基态能量。结果表明本文给出的方法是对直接超球谐广义Ｌａｇｕｅｒｒｅ函数展开法（ＨＨ－ＧＬＦ）的一个非常有效的改进。     

一类球函数加法公式在多球体散射中的应用

首先利用格林函数的双中心球坐标展开式得到了一类球函数加法公式。对于多球体声学系统,可应用该加法公式将空间声场相对于每一个球体中心展开,这样可以很方便地利用每个球体的边界条件来研究多球体系统的声学散射问题。研究了两球体系统在不同边界条件下的散射声场,每个球的散射声场可通过求解由双重级数和耦合的两个无穷方程组得到。最后引入了形函数的定义,计算了两球体系统在平面波入射下的形函数,从而通过与现有文献的数值对比验证了本文理论公式的正确性。     

卷云冰晶粒子散射相函数的展开系数研究

冰晶粒子散射相函数的多项式展开可以应用于卷云条件下大气辐射传输模式的计算。本文利用广义球函数对表面严重粗糙的冰晶粒子相函数进行展开,并对表面严重粗糙的实心棱柱模型、实心棱柱聚合物模型和一般种类混合模型3种冰晶粒子的展开系数特性进行分析研究,数值计算结果表明了广义球函数对表面严重粗糙的冰晶粒子多项式展开的有效性。     

球对称折射率分布及其光程

近年来人们对变折射率分布中的球对称分布的研究日渐重视。本文进一步深入分析了球对称折射率分布,证明球对称分布中光线的倾斜度核心值即为其积分不变量;一个令人惊异的结果是,麦克斯韦透镜中任意共轭点之间的光程都相等,并可用分布参数表为π/2n₀a。     

The spatial unmasking of speech: evidence for within-channel processing of interaural time delay

Across-frequency processing by common interaural time delay (ITD) in spatial unmasking was investigated by measuring speech reception thresholds (SRTs) for high- and low-frequency bands of target speech presented against concurrent speech or a noise masker. Experiment 1 indicated that presenting one of these target bands with an ITD of +500 micros and the other with zero ITD (like the masker) provided some release from masking, but full binaural advantage was only measured when both target bands were given an ITD of + 500 micros. Experiment 2 showed that full binaural advantage could also be achieved when the high- and low-frequency bands were presented with ITDs of equal but opposite magnitude (+/- 500 micros). In experiment 3, the masker was also split into high- and low-frequency bands with ITDs of equal but opposite magnitude (+/-500 micros). The ITD of the low-frequency target band matched that of the high-frequency masking band and vice versa. SRTs indicated that, as long as the target and masker differed in ITD within each frequency band, full binaural advantage could be achieved. These results suggest that the mechanism underlying spatial unmasking exploits differences in ITD independently within each frequency channel.     

Separation of concurrent broadband sound sources by human listeners

The effect of spatial separation on the ability of human listeners to resolve a pair of concurrent broadband sounds was examined. Stimuli were presented in a virtual auditory environment using individualized outer ear filter functions. Subjects were presented with two simultaneous noise bursts that were either spatially coincident or separated (horizontally or vertically), and responded as to whether they perceived one or two source locations. Testing was carried out at five reference locations on the audiovisual horizon (0 degrees, 22.5 degrees, 45 degrees, 67.5 degrees, and 90 degrees azimuth). Results from experiment 1 showed that at more lateral locations, a larger horizontal separation was required for the perception of two sounds. The reverse was true for vertical separation. Furthermore, it was observed that subjects were unable to separate stimulus pairs if they delivered the same interaural differences in time (ITD) and level (ILD). These findings suggested that the auditory system exploited differences in one or both of the binaural cues to resolve the sources, and could not use monaural spectral cues effectively for the task. In experiments 2 and 3, separation of concurrent noise sources was examined upon removal of low-frequency content (and ITDs), onset/offset ITDs, both of these in conjunction, and all ITD information. While onset and offset ITDs did not appear to play a major role, differences in ongoing ITDs were robust cues for separation under these conditions, including those in the envelopes of high-frequency channels.     

Similar patterns of learning and performance variability for human discrimination of interaural time differences at high and low frequencies

Sound source localization on the horizontal plane is primarily determined by interaural time differences (ITDs) for low-frequency stimuli and by interaural level differences (ILDs) for high-frequency stimuli, but ITDs in high-frequency complex stimuli can also be used for localization. Of interest here is the relationship between the processing of high-frequency ITDs and that of low-frequency ITDs and high-frequency ILDs. A few similarities in human performance with high- and low-frequency ITDs have been taken as evidence for similar ITD processing across frequency regions. However, such similarities, unless accompanied by differences between ITD and ILD performance on the same measure, could potentially reflect processing attributes common to both ITDs and ILDs rather than to ITDs only. In the present experiment, both learning and variability patterns in human discrimination of ITDs in high-frequency amplitude-modulated tones were examined and compared to previously obtained data with low-frequency ITDs and high-frequency ILDs. Both patterns for high-frequency ITDs were more similar to those for low-frequency ITDs than for high-frequency ILDs. These results thus add to the evidence supporting similar ITD processing across frequency regions, and further suggest that both high- and low-frequency ITD processing is less modifiable and more noisy than ILD processing.     

Sequential streaming due to manipulation of interaural time differences

The effect of apparent spatial location on sequential streaming was investigated by manipulating interaural time differences (ITDs). The degree of obligatory stream segregation was inferred indirectly from the threshold for detecting a rhythmic irregularity in an otherwise isochronous sequence of interleaved "A" and "B" tones. Stimuli were bandpass-filtered harmonic complexes with a 100-Hz fundamental. The A and B tones had equal but opposite ITDs of 0, 0.25, 0.5, 1, or 2 ms and had the same or different passbands. The passband ranges were 1250-2500 Hz and 1768-3536 Hz in experiment 1, and 353-707 Hz and 500-1000 Hz in experiment 2. In both experiments, increases in ITD led to increases in threshold, mainly when the passbands of A and B were the same. The effects were largest for ITDs above 0.5 ms, for which rhythmic irregularities in the timing of the A or B tones alone may have disrupted performance. It is concluded that the differences in apparent spatial location produced by ITD have only weak effects on obligatory streaming.     

Spatial cues alone produce inaccurate sound segregation: the effect of interaural time differences

To clarify the role of spatial cues in sound segregation, this study explored whether interaural time differences (ITDs) are sufficient to allow listeners to identify a novel sound source from a mixture of sources. Listeners heard mixtures of two synthetic sounds, a target and distractor, each of which possessed naturalistic spectrotemporal correlations but otherwise lacked strong grouping cues, and which contained either the same or different ITDs. When the task was to judge whether a probe sound matched a source in the preceding mixture, performance improved greatly when the same target was presented repeatedly across distinct distractors, consistent with previous results. In contrast, performance improved only slightly with ITD separation of target and distractor, even when spectrotemporal overlap between target and distractor was reduced. However, when subjects localized, rather than identified, the sources in the mixture, sources with different ITDs were reported as two sources at distinct and accurately identified locations. ITDs alone thus enable listeners to perceptually segregate mixtures of sources, but the perceived content of these sources is inaccurate when other segregation cues, such as harmonicity and common onsets and offsets, do not also promote proper source separation.     

Sensitivity to binaural timing in bilateral cochlear implant users

Various measures of binaural timing sensitivity were made in three bilateral cochlear implant users, who had demonstrated moderate-to-good interaural time delay (ITD) sensitivity at 100 pulses-per-second (pps). Overall, ITD thresholds increased at higher pulse rates, lower levels, and shorter durations, although intersubject differences were evident. Monaural rate-discrimination thresholds, using the same stimulation parameters, showed more substantial elevation than ITDs with increased rate. ITD sensitivity with 6000 pps stimuli, amplitude-modulated at 100 Hz, was similar to that with unmodulated pulse trains at 100 pps, but at 200 and 300 Hz performance was poorer than with unmodulated signals. Measures of sensitivity to binaural beats with unmodulated pulse-trains showed that all three subjects could use time-varying ITD cues at 100 pps, but not 300 pps, even though static ITD sensitivity was relatively unaffected over that range. The difference between static and dynamic ITD thresholds is discussed in terms of relative contributions from initial and later arriving cues, which was further examined in an experiment using two-pulse stimuli as a function of interpulse separation. In agreement with the binaural-beat data, findings from that experiment showed poor discrimination of ITDs on the second pulse when the interval between pulses was reduced to a few milliseconds.     

The effect of an additional reflection in a precedence effect experiment

Studies on the precedence effect typically utilize a two-source paradigm, which is not realistic relative to real world situations where multiple reflections exist. A step closer to multiple-reflection situations was studied using a three-source paradigm. Discrimination of interaural time differences (ITDs) was measured for one-, two-, and three-source stimuli, using clicks presented over headphones. The ITD was varied in either the first, second, or the third source. The inter-source intervals ranged from 0-130 ms. A perceptual weighting model was extended to incorporate the three-source stimuli and used to interpret the data. The effect of adding a third source could mostly, but not entirely, be understood by the interaction of effects observed in the precedence effect with two sources. Specifically, for delays between 1 and 8 ms, the ITD information of prior sources was typically weighted more heavily than subsequent sources. For delays greater than 8 ms, subsequent sources were typically weighted slightly more heavily than prior sources. However, there were specific conditions that showed a more complex interaction between the sources. These findings suggest that the two-source paradigm provides a strong basis for understanding how the auditory system processes reflections in spatial hearing tasks.     

Manipulating the "straightness" and "curvature" of patterns of interaural cross correlation affects listeners' sensitivity to changes in interaural delay

The purpose of this study was to test the hypothesis that stimuli characterized by "straight" trajectories of their patterns of cross correlation foster greater sensitivity to changes in interaural temporal disparities (ITDs) than do stimuli characterized by more "curved" trajectories of their patterns of cross correlation. To do so, sensitivity to changes in ITD was measured, as a function of duration, using a set of "reference" stimuli that yielded differing relative amounts of straightness within their patterns of cross correlation while keeping the dominant trajectory at or near midline. The relative amounts of straightness were manipulated by employing specific combinations of bandwidth, ITD, and interaural phase disparity (IPD) of Gaussian noises centered at 500 Hz. The results were consistent with expectations in that the patterning of the threshold ITDs revealed increasingly poorer sensitivity as greater and greater curvature was imposed on the dominant, "midline," trajectory. The variations in threshold ITD across the stimulus conditions can be accounted for quite well quantitatively by assuming either that the listeners based their judgments on changes in the position of the most central peak of the cross-correlation function or that they based their judgments on changes in the centroid of a second-level cross-correlation function. In a second experiment, binaural detection was measured using a subset of the reference stimuli as maskers. As expected, sensitivity was poorest with the maskers characterized by the greatest curvature, which were also those having the lowest interaural correlation.     

Lateralization and detection of pulse trains with alternating interaural time delays

The effect of onset interaural time differences (ITDs) on lateralization and detection was investigated for broadband pulse trains 250 ms long with a binaural fundamental frequency of 250 Hz. Within each train, ITDs of successive binaural pulse pairs alternated between two of three values (0 micros, 500 micros left-leading, and 500 micros right-leading) or were invariant. For the alternating conditions, the experimental manipulation was the choice of which of two ITDs was presented first (i.e., at stimulus onset). Lateralization, which was estimated using a broadband noise pointer with a listener adjustable interaural delay, was determined largely by the onset ITD. However, detection thresholds for the signals in left-leading or diotic continuous broadband noise were not affected by where the signals were lateralized. A quantitative analysis suggested that binaural masked thresholds for the pulse trains were well accounted for by the level and phase of harmonic components at 500 and 750 Hz. Detection thresholds obtained for brief stimuli (two binaural pulse or noise burst pairs) were also independent of which of two ITDs was presented first. The control of lateralization by onset cues appears to be based on mechanisms not essential for binaural detection.     

The acoustical cues to sound location in the rat: measurements of directional transfer functions

The acoustical cues for sound location are generated by spatial- and frequency-dependent filtering of propagating sound waves by the head and external ears. Although rats have been a common model system for anatomy, physiology, and psychophysics of localization, there have been few studies of the acoustical cues available to rats. Here, directional transfer functions (DTFs), the directional components of the head-related transfer functions, were measured in six adult rats. The cues to location were computed from the DTFs. In the frontal hemisphere, spectral notches were present for frequencies from approximately 16 to 30 kHz; in general, the frequency corresponding to the notch increased with increases in source elevation and in azimuth toward the ipsilateral ear. The maximum high-frequency envelope-based interaural time differences (ITDs) were 130 mus, whereas low-frequency (<3.5 kHz) fine-structure ITDs were 160 mus; both types of ITDs were larger than predicted from spherical head models. Interaural level differences (ILDs) strongly depended on location and frequency. Maximum ILDs were <10 dB for frequencies <8 kHz and were as large as 20-40 dB for frequencies >20 kHz. Removal of the pinna eliminated the spectral notches, reduced the acoustic gain and ILDs, altered the acoustical axis, and reduced the ITDs.