Based on the decorrelation and frequency-band partitions of DWT for long memory process （LMP）

a ap-proximating covariance matrix was given and a related transform was constructed

which could transform an IID stochas-tic vector into a sample realization of fractionally differenced （FD） process. To carry out this transform

a physical quan-tity called sub-band variance was proposed and computed under the FD parameters specified. At last

construction sam-ples were compared with theoretical model

and their statistical properties were checked in two ways. Computing results validate that the algorithm presented is feasible

rational and effective in a statistical sense.