This paper introduces a collection of scaling methods for generating 2 N-point DCT-II approximations based on N-point low-complexity transformations. Such scaling is based on the Hou recursive matrix factorization of the exact 2 N-point DCT-II matrix. Encompassing the widely employed Jridi-Alfalou-Meher scaling method, the proposed techniques are shown to produce DCT-II approximations that outperform the transforms resulting from the JAM scaling method according to total error energy and mean squared error. Orthogonality conditions are derived and an extensive error analysis based on statistical simulation demonstrates the good performance of the introduced scaling methods. A hardware implementation is also provided demonstrating the competitiveness of the proposed methods when compared to the JAM scaling method.

中文翻译：

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DCT-II 近似的低复杂度缩放方法


本文介绍了基于 N 点低复杂度变换生成 2 个 N 点 DCT-II 近似的缩放方法集合。这种缩放基于精确 2 N 点 DCT-II 矩阵的 Hou 递归矩阵分解。涵盖广泛采用的 Jridi-Alfalou-Meher 缩放方法，所提出的技术被证明可以产生 DCT-II 近似，根据总误差能量和均方误差，其性能优于 JAM 缩放方法产生的变换。导出了正交条件，并且基于统计模拟的广泛误差分析证明了所引入的缩放方法的良好性能。还提供了硬件实现，证明了所提出的方法与 JAM 缩放方法相比的竞争力。