音频压缩中3种整数型MDCT变换的比较

Comparison of three IntMDCT algorithms in audio compression

为了快速计算整数型改进的离散余弦变换(IntMDCT),构造了基于提升变换、模变换以及无穷范数旋转变换的3种计算12点IntMDCT的算法.首先将12点MDCT转化为6点Ⅳ型离散余弦变换(DCT-Ⅳ),并将后者分解为7个Givens旋转变换的乘积;然后分别利用提升变换算法、模变换算法和无穷范数旋转变换算法实现Givens旋转变换的整数型近似计算;最后,对这3种算法在语音信号无损和有损压缩中的运行速度和计算精确度进行比较.实验结果表明,在这3种算法中,基于模变换的IntMDCT算法的运行速度最快;基于无穷范数旋转变换的IntMDCT算法的计算精度最高,并在有损音频压缩中获得的信噪比最高.

In order to improve the computation efficiency of the integer modified discrete cosine transform （IntMDCT）, three algorithms based on the lifting scheme, modulo transform and infinity norm rotation transform are formulated respectively for computing the 12-point IntMDCT. First, the12-point IntMDCT is converted into the 6-point type-IV discrete cosine transform （DCT-IV）, which is then factorized into a product of 7 Givens rotation matrices. The integer type Givens rotation ma- trices are approximated by lifting scheme, modulo transform and infinity norm rotation transform,respectively, Finally, the speed and accuracy of these three IntMDCT algorithms are compared in both lossless and lossy audio compression. The experimental results show that in the three algo- rithms, the IntMDCT algorithm based on the modulo transform has the highest computation speed. The IntMDCT algorithm based on the infinity norm rotation transform has the highest accuracy, and can achieve the highest signal to noise ratio （SNR） in lossy audio compression.