Downsampling with Boundary Correction
blo = CDJVDyadDown(bhi,F,LEF,REF)
1-d signal, at fine scale
filter
left edge filter bank
right edge filter bank
1-d signal, at coarse scale
CDJV have developed an algorithm for wavelets on the interval which preserves the orthogonality, vanishing moments, smoothness and compact support of Daubechies wavelets on the line.
The CDJV algorithm for wavelets on the interval involves filtering combined with upsampling and downsampling, just like the algorithm on the line and circle. However, the filtering is not convolutional at the edges; instead special edge-filter matrices are applied. CDJVDyadDown implements the downsampling with edge-adjustment.
CDJV -- Cohen, Daubechies, Jawerth and Vial, 1992.