기저의 길이 L=2M인 경우 무손실 행렬의 분해를 이용한 고속 M-대역 이산 웨이브렛 변환 알고리즘

A fast M-band discrete wavelet transform algorithm using factorization of lossless matrix when the length of bases equals to 2M

The fast implementation algorithm of M-band discrete wavelet transform is propsed using the factorization of lossless matrix when the length of discrete orthogonal wavelet bases equals to 2M. In computational complexity when direct filtering method is employed, the number of multiplicationand addition is (2M$^{2}$) and (2M$^{2}$ -M), respectively. But by proposed algorithm, it can be reduced to (M$^{2}$+M) and (M$^{2}$+2M-1), respectively. and it is possible to reduce the compuatational complexity further when unitary matrix employed to design the discrete or thogonal wavelet basis has the fast algorithm.