离散正弦变换-Ⅱ的一种快速递归算法

A Fast Recursive Algorithm for the Discrete Sine Transform-Ⅱ

本文推导了离散正弦变换-Ⅱ(DST-Ⅱ)的递归特性,由此提出了DST-Ⅱ的一种快速递归算法,分析了运算工作量,给出了一般算法流图,并与DST-Ⅱ的其他快速算法作了比较。结果表明,本文提出的算法所需运算量最少,可进行原位计算,它用余弦作乘子,是一种数值稳定的算法。而且算法结构简单规则,适于并行处理,易用硬件或软件实现。鉴于这些特点,DST-Ⅱ的快速递归算法可望在实际中得到广泛的应用。

The recursiveness of the discrete sine transform-Ⅱ (DST)is derived in this paper. It follows that a fast recursive algorithm for the DST-Ⅱ is proposed. The computational complexity is analyzed and the general algorithm flow graph is given. A comparison of this algorithm is made with other fast algorithms for the DST-Ⅱ. It is shown that the proposed algorithm requires the lowest number of arithmetic operations and allows in-place computation. It use cosine as multipliers and is a numerically stable algorithm. Besides, the structure of the algorithm is simple and regular, it is applicable for parallel processing and it is easy to be implemented in either hardware or software. In view of the above-mentioned advantages, the fast recursive algorithm for the DST-Ⅱ will be expected to find wide applications in practice.