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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。
This paper deduces the recursive property of Discrete Sine Transform-Ⅱ (DST-Ⅱ), and proposes a fast recursive algorithm for DST-Ⅱ. The computational workload is analyzed and a general algorithm flow graph is given. The other fast algorithms are compared. The results show that the algorithm proposed in this paper requires a minimum amount of computation and can be calculated in situ. It uses a cosine as a multiplier and is a numerical stable algorithm. And the algorithm structure is simple and rules, suitable for parallel processing, easy to use hardware or software. In view of these characteristics, DST-Ⅱ fast recursive algorithm is expected to be widely used in practice.