Fig. 4

Filter-bank interpretation of the fast algorithm we proposed. a A fast linear canonical wavelet transform is computed with a cascade of filtering with \({\bar h_{M,0}}(k)\) and \({\bar h_{M,1}}(k)\) in the LCT domain followed by a factor 2 subsampling. Note that the linear canonical convolution is used here according to (53a) and (53b). b A fast inverse linear canonical wavelet transform reconstructs progressively each a _M,j by inserting zeroes between samples of a_M,j+1 and d_M,j+1, filtering in the LCT domain and adding the outputs. Note that the linear canonical convolution is used here according to (57)