This paper introduces a new family of optimal transform coders (TC) based on the generalized triangular decomposition (GTD) developed by Jiang, et al. The new class contains the Karhunen-Loeve transform (KLT), and the prediction-based lower triangular transform (PLT) introduced by Phoong and Lin, as special cases. The coding gain of the entire family, with optimal bit allocation, is equal to that of the KLT (equivalently the PLT). Even though the original PLT was only applicable for blocked versions of scalar wide sense stationary (WSS) processes, the GTD based family includes members which are natural extensions of the PLT.
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As special cases, we obtain the boundedness of fractional operators.
特别的，我们得到了分数次积分算子的有界性。
Most economic behavior can be viewed as special cases of game theory.
大多数经济行为都可以看作博弈论的一个特殊案例。
Our results contains previous locally risk-minimizing hedging as special cases.
我们的结果包含了以前的局部风险最小对冲策略。
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