Gardner Timothy J, Magnasco Marcelo O
Center for Studies in Physics and Biology, The Rockefeller University, 1230 York Avenue, New York, NY 10021.
Proc Natl Acad Sci U S A. 2006 Apr 18;103(16):6094-9. doi: 10.1073/pnas.0601707103. Epub 2006 Apr 6.
Auditory neurons preserve exquisite temporal information about sound features, but we do not know how the brain uses this information to process the rapidly changing sounds of the natural world. Simple arguments for effective use of temporal information led us to consider the reassignment class of time-frequency representations as a model of auditory processing. Reassigned time-frequency representations can track isolated simple signals with accuracy unlimited by the time-frequency uncertainty principle, but lack of a general theory has hampered their application to complex sounds. We describe the reassigned representations for white noise and show that even spectrally dense signals produce sparse reassignments: the representation collapses onto a thin set of lines arranged in a froth-like pattern. Preserving phase information allows reconstruction of the original signal. We define a notion of "consensus," based on stability of reassignment to time-scale changes, which produces sharp spectral estimates for a wide class of complex mixed signals. As the only currently known class of time-frequency representations that is always "in focus" this methodology has general utility in signal analysis. It may also help explain the remarkable acuity of auditory perception. Many details of complex sounds that are virtually undetectable in standard sonograms are readily perceptible and visible in reassignment.
听觉神经元保留着有关声音特征的精确时间信息，但我们并不清楚大脑是如何利用这些信息来处理自然界中快速变化的声音的。关于有效利用时间信息的简单论证使我们将重分配类时频表示法视为听觉处理的一种模型。重分配时频表示法能够精确地追踪孤立的简单信号，其精度不受时频不确定性原理的限制，但缺乏一个通用理论阻碍了它们在复杂声音中的应用。我们描述了白噪声的重分配表示，并表明即使是频谱密集的信号也会产生稀疏的重分配：这种表示会坍缩到一组排列成泡沫状图案的细线上。保留相位信息可以重建原始信号。我们基于重分配对时间尺度变化的稳定性定义了一个“一致性”概念，它能为一大类复杂混合信号产生精确的频谱估计。作为目前唯一已知的始终“聚焦”的时频表示法，这种方法在信号分析中具有普遍用途。它或许还能帮助解释听觉感知的非凡敏锐度。许多在标准声谱图中几乎无法检测到的复杂声音细节，在重分配图中却很容易被感知和看到。
