Study on Decomposition & Smooth Reconstruction for Wavelets
Xu Zhang · Central China Electric Power · 2000
This paper presents a transform matrix B [n×n]for decomposing the sampled signal F [n]into Haar Wavelets series coefficients C [n]where n is exponent of 2.The invrse transform matrix B-1=BT. So the wavelet taansform matrix method is quite convenient for decomposing C=B. F or reconstucting F=BT.C.Ifwe let C[k] =0,where k from(n/4+1) to n,then reconstruchng the new funchon F1 [n],and remainning ouly n/4 numbers in another fonchon Y [k] =F1 [4k] .This Y [n/4]signal is comperssed with 4 hmes from the sampled signal F[n],it would be smoothy than before.Some examples are presented with iliustration.