Approximate methods have been considered as a means to the evaluation of discrete transforms. In this work, we propose and analyze a class of integer transforms for the discrete Fourier, Hartley, and cosine transforms (DFT, DHT, and DCT), based on simple dyadic rational approximation methods. The introduced method is general, applicable to several block-lengths, whereas existing approaches are usually dedicated to specific transform sizes. The suggested approximate transforms enjoy low multiplicative complexity and the orthogonality property is achievable via matrix polar decomposition. We show that the obtained transforms are competitive with archived methods in literature. New 8-point square wave approximate transforms for the DFT, DHT, and DCT are also introduced as particular cases of the introduced methodology.

中文翻译：

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离散正弦变换的整数近似方法

近似方法已被认为是评估离散变换的一种手段。在这项工作中，我们基于简单的二元有理近似方法提出并分析了离散傅立叶、哈特利和余弦变换（DFT、DHT 和 DCT）的一类整数变换。引入的方法是通用的，适用于多个块长度，而现有方法通常专用于特定的变换大小。建议的近似变换具有低乘法复杂度，并且正交性可通过矩阵极坐标分解实现。我们表明，获得的变换与文献中的存档方法具有竞争力。还介绍了 DFT、DHT 和 DCT 的新 8 点方波近似变换，作为所介绍方法的特殊情况。