pX[0]x[O] oWApx[1]x[4] 0--1Wop X[2]x[2] 0WWN X[3]x[6] 0-1WX[4]x[1]oWAWNFigure 9.10X[5]x[5] 0-1woWRX[6]x[3] 0woWRWAX[7]x[7] o-11timesof complexmultiplication:1time /butterfly computatio n *N/2butterfly computatio ns/stage *log2stagetimes of complex addition :2 times / butterfly computatio n * N / 2butterfly computatio ns / stage * log2 stagestrongpoint:in-placecomputationsshortcoming:non-sequentialaccess ofdata
Figure 9.10 2 times / butterfly computatio n * / 2butterfly computatio ns /stage *log stage times of complex addition 1 time / butterfly computatio n * / 2 butterfly computatio ns /stage *log stage times of complex multiplica tion 2 2 N N N N ： ： strongpoint：in-place computations shortcoming：non-sequential access of data
comparetheoperationquantity复数乘法欣数直接基2FFT車二
compare the operation quantity
alternativeforms:Figure9.140X[0]x[0] owoX[4]x[1] We0X[2]x[2] α-weWX[6]x[3] owo0 X[1]x[4] o-wWioX[5]x[5] oWA0X[3]x[6] o-WWAWX[7]x[7] o-1-1strongpointin-placecomputationsshortcoming: non-sequential access of data
alternative forms： Figure 9.14 strongpoint：in-place computations shortcoming：non-sequential access of data
Figure 9.150 X[0]x[0] 0-we.X[1]x[1] c-01WNX[2]x[2] -WWNp X[3]x[3] 0wb X[4]x[4] 0wWR X[5]x[5] wA2Wx[6] o X[6]-1M-1wWRWNx[7] o-F0X[7]-1-1-1shortcoming: not in-place computationnon-sequential access of data
Figure 9.15 shortcoming：not in-place computation non-sequential access of data
Figure 9.16x[0] o-X[0]wwN-WNX[1]x[4] 0-x[2] 0X[2]wwNW x[3]x[6] 0-6 X[4]x[1] 0wWNWAX[5]x[5] 051-1 X[6]x[3] o-1WWRWX[7]x[7] 0-1-1-1shortcoming:not in-place computationsequential access of datastrongpoint:
Figure 9.16 shortcoming：not in-place computation strongpoint: sequential access of data