This paper introduces a collection of scaling methods for generating $2N$-point DCT-II approximations based on $N$-point low-complexity transformations. Such scaling is based on the Hou recursive matrix factorization of the exact $2N$-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.

翻译：本文提出了一系列缩放方法，用于基于N点低复杂度变换生成2N点DCT-II近似。此类缩放基于精确2N点DCT-II矩阵的Hou递归矩阵分解。所提出的技术涵盖了广泛使用的Jridi-Alfalou-Meher缩放方法，并表明其产生的DCT-II近似在总误差能量和均方误差方面优于JAM缩放方法生成的变换。本文推导了正交性条件，并通过基于统计仿真的广泛误差分析证明了所引入缩放方法的良好性能。此外，还提供了硬件实现，展示了所提方法相较于JAM缩放方法的竞争力。