热通道及相关热源在时频平面上的充水定理
Waterfilling Theorems in the Time-Frequency Plane for the Heat Channel and a Related Source
摘要：
热通道是一个线性时变滤波器，具有加性高斯白噪声（AWGN），其容量在时频平面上表现为注水现象。类似地，相关非平稳源的率失真函数的特征在于在时频平面中的反向注水。源由与之前相同的LTV滤波器的高斯白噪声响应形成。这两个注水定理的证明依赖于一个特定的Szego定理与过滤器相关联的正定算子。给出了Szego定理的一个基本自含的证明。充水定理与Gallager和Berger的经典结果进行了比较。在非平稳源的情况下，可以观察到经典功率谱密度（PSD）的一部分被Wigner-Ville谱（WVS）所占据。
英文摘要：
The capacity of the heat channel, a linear time-varying (LTV) filter with additive white Gaussian noise (AWGN), is characterized by waterfilling in the time-frequency plane. Similarly, the rate distortion function for a related nonstationary source is characterized by reverse waterfilling in the time-frequency plane. The source is formed by the white Gaussian noise response of the same LTV filter as before. The proofs of both waterfilling theorems rely on a specific Szego theorem for a positive definite operator associated with the filter. An essentially self-contained proof of the Szego theorem is given. The waterfilling theorems compare well with classical results of Gallager and Berger. In case of the nonstationary source it is observed that the part of the classical power spectral density (PSD) is taken by the Wigner-Ville spectrum (WVS).
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