【摘要】 给出一种采用快速傅里对变换（ＦＦＴ）的反卷积算法。对于Ｎ维图卷积矩阵，所需复乘／除次数约为Ｎ（ｌｏｇ２Ｎ＋１），复加次数约为。对卷积矩阵维数Ｎ＝２ｃ的反卷积计算，在不同ＦＦＴ时可将Ｎ维图卷积矩阵求逆转变成解，２阶线性议程组，所需乘法次数约为。更多还原

【Abstract】 To my best knowledge,there is no paper published in China, if not in the world, on deconvolution method for system identification and signal reconstruction. 111 - conditioned equationssometimes make trouble in system identification and signal reconstruction. When conditions derived by me and given as equations (15) and (16)are satisfied, no ill-conditioned equations willbe encountered when my deconvolution method is used. The satisfaction of equations (15) and(16)do not gurantee that ill-conditioned equations will not be encountered when other methodsnow avilable are used. In my deconvolution method, dimension of cyclic matrix is taken as integral power of number 2. Obviously it corresponds to N linear algebra equations that need to besolved. In my method, the matrix can be successively decomposed into matrices with dimensionsof N/2, N/4, etc. For simplicity, N is taken to be 4, and the inverse matrix is computable withequations (11) through (14). My deconvolution method requires only (3/2) log2N Nmultiplicationsfor computing the inverse of cyclic matrix as against N3 /42 multiplications required by Winograd’s method [1].更多还原