摘要
本文利用多项式变换和切匹雪夫多项式变换计算2-D DCT来推导2-D DCT的乘法复杂性。证明在有理数域上计算2~m×2~m 2-D DCT所需的最小实数乘法次数为2^(2m+1)-m2~m-2^(m+1),并说明利用多项式变换和切匹雪夫多项式变换计算2-D DCT的乘法复杂性是相同的。
In this paper, we develop the multiplicative complexity of the two-dimensional discrete cosine
transform of length N=2~m by use of the polynomial transform computation and the Chebyshev polynomial trans-
form computation. We prove that the minimal number of real multiplieations necessary to compute a 2~m×2~m
two-dimensional discrete cosine transformover the field Q of rational numbers is equal to 2^(2m+1)-m2~m-2^(m+1).
The method of derivation is shown that the polynomial transform computation and the Chebryshev polynomial
transform computation have the same multiplicative complexity.
出处
《信号处理》
CSCD
北大核心
1992年第2期105-111,共7页
Journal of Signal Processing
基金
国家自然科学基金资助项目
