Implementation of the discrete wavelet transform and associated processing functions.

Usage: import wavelets as wl:

wl.multires (Multiple-resolution analysis) repeatedly decomposes the approximate coefficients. Because the approximate coefficients represent the low frequency part of the signal, each level analyses a lower frequency portion of the signal.

[signal]──┬─>[cD1] ┄┄┄┄┄┄┄┄┄┄┄┄┄┄[cD1]        level 1
          └─>[cA1]──┬─>[cD2]┄┄┄┄┄[cD2]        level 2
                    └─>[cA2]──┬─>[cD3]        level 3
                              └─>[cA3]

Each decomposition splits the signal into a higher and lower frequency component, so the frequencies spanned by the final sets of coefficients e.g.:

cD1: 1000 - 500 Hz
cD2: 500 - 250 Hz
cD3: 250 - 125 Hz
cA3: 125 - 0 Hz

wl.inverseMultires reconstructs the original signal from the set of coefficients generated by multi-resolution analysis. In reverse to multi-resolution decomposition, it iteratively reconstructs each approximate coefficient array from the lower level

[cD1]──────────────────────┬─>[signal]
[cD2]────────────┬─>[cA1]──┘
[cD3]──┬─>[cA2]──┘
[cA3]──┘