The colors in the model indicate the relative sample rates of the data. Note that many of the intervening blocks process multiple rates simultaneously. In a multirate time-flow environment, such as Simulink, the data is conceptually infinite in length, and the data alignment cannot be performed by indexing. Instead, delay elements are introduced after the analysis filter bank to achieve data alignment. Also, to compare the output signal with the input, additional delays are introduced into the input signal path.
Data alignment is a significant aspect of a practical, real-time implementation.
An important property of wavelet filter banks is perfect reconstruction . That is, if we connect the output of the analysis filter bank to the input of the synthesis filter bank and use the proper delays for alignment, then the output of the system is identical to the input. The thresholding is carried out in Fig. 1 using a dead-zone transfer function that removes coefficients with values less than a specified level. The output may be subtracted from the input to generate a residual signal and is useful for determining the level of de-noising.