Discrete cosine transforms are widely used in smart radioelectronic systems for processing and analysis of incoming information. The popularity of using these transform is explained by the presence of fast algorithms that minimize the computational and hardware complexity of their implementation. Type-IV discrete cosine transform occupies a special place in the list of the specified transformations. This article proposes several algorithmic solutions for implementing the type-IV discrete cosine transform. The effectiveness of the proposed solutions is explained by the possibility of factorization of the DCT-IV matrix, which leads to a decrease in computational and implementation complexity. A set of completely parallel type-IV DCT algorithms for small lengths of signal sequences (N = 2, 3, 4, 5, 6, 7, 8, 9) is presented.

中文翻译：

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用于降低乘法复杂度的 IV 型离散余弦变换的小型算法

离散余弦变换广泛用于智能无线电电子系统，用于处理和分析传入信息。使用这些变换的流行是由于快速算法的存在将其实现的计算和硬件复杂性降至最低。类型 IV 离散余弦变换在指定变换列表中占有特殊的位置。本文提出了几种用于实现类型 IV 离散余弦变换的算法解决方案。所提出的解决方案的有效性可以通过对 DCT-IV 矩阵进行分解的可能性来解释，这导致计算和实现复杂性的降低。提出了一组用于小长度信号序列 (N = 2, 3, 4, 5, 6, 7, 8, 9) 的完全并行的 IV 型 DCT 算法。