# 王小庆,伍家松,舒华忠.一种DTT域的二维线性卷积算法[J].东南大学学报(自然科学版),2012,42(3):424-427.[doi:10.3969/j.issn.1001-0505.2012.03.006] 　Wang Xiaoqing,Wu Jiasong,Shu Huazhong.Two dimensional linear convolution in discrete trigonometric transform domain[J].Journal of Southeast University (Natural Science Edition),2012,42(3):424-427.[doi:10.3969/j.issn.1001-0505.2012.03.006] 点击复制 一种DTT域的二维线性卷积算法( ) 分享到： var jiathis_config = { data_track_clickback: true };

42

2012年第3期

424-427

2012-05-20

## 文章信息/Info

Title:
Two dimensional linear convolution in discrete trigonometric transform domain

Author(s):
Laboratory of Image Science and Technology, Southeast University, Nanjing 210096, China

Keywords:

TP301.5
DOI:
10.3969/j.issn.1001-0505.2012.03.006

Abstract:
A novel algorithm for 2-D linear convolution in the discrete trigonometric transform(DTT)domain is proposed. First, the relationship between 2-D type-Ⅱ discrete cosine transform(DCT-Ⅱ)with a block size of N1×N2 and the 2-D discrete Fourier transform( DFT )with a block size of 2N1×2N2 is derived, and the representation of the convolution multiplication properties of 2-D DFT is converted into the corresponding 2-D DTT. Secondly, the explicit expression of the relationship between the DCT-Ⅱ of the output signal and the DTT of the input signal for the linear filter is given. Finally, the computational complexity of the proposed algorithm is analyzed. The results show that the proposed algorithm has lower computational complexity than the common spatial domain based method when the filter size is larger than 5×5. In addition, the algorithm is more efficient than the DFT domain filtering algorithm if the DCT-Ⅱ coefficients of the translated input signal are known.