具有减少算术运算次数的IV型DCT、DST和MDCT算法
Type-IV DCT, DST, and MDCT algorithms with reduced numbers of arithmetic operations
AI总结：
提出通过将DCT视为8N长度DFT的特例并利用对称性，从改进的快速傅里叶变换算法中剪枝冗余操作，从而在保持数值精度的前提下降低DCT-IV、DST-IV和MDCT的实数乘法和加法次数。
摘要：
我们提出了用于IV型离散余弦变换（DCT-IV）和离散正弦变换（DST-IV），以及改进的离散余弦变换（MDCT）及其逆变换的算法，这些算法在保持数值精度的同时，实现了比先前发表的算法更低的实数乘法和加法次数。渐近地，对于2的幂次变换大小N，运算次数从约2NlogN减少到约(17/9)NlogN，并且对于所有N > 4，精确次数严格降低。这些结果通过将DCT视为长度为8N的DFT的特例（具有某些对称性），然后从最近改进的快速傅里叶变换算法（基于共轭对分裂基算法的递归重新缩放）中剪枝冗余操作而得到。DST-IV和MDCT的改进算法直接来自DCT-IV的改进计数。
英文摘要：
We present algorithms for the type-IV discrete cosine transform (DCT-IV) and discrete sine transform (DST-IV), as well as for the modified discrete cosine transform (MDCT) and its inverse, that achieve a lower count of real multiplications and additions than previously published algorithms, without sacrificing numerical accuracy. Asymptotically, the operation count is reduced from ~2NlogN to ~(17/9)NlogN for a power-of-two transform size N, and the exact count is strictly lowered for all N > 4. These results are derived by considering the DCT to be a special case of a DFT of length 8N, with certain symmetries, and then pruning redundant operations from a recent improved fast Fourier transform algorithm (based on a recursive rescaling of the conjugate-pair split radix algorithm). The improved algorithms for DST-IV and MDCT follow immediately from the improved count for the DCT-IV.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
