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PyWavelets
Matlab wavelet compatibility
If we decide we want to have all of the Matlab wavelets available, here is the list available in Matlab r2015b:
>>> waveletfamilies('n')
===================================
Haar haar
===================================
Daubechies db
------------------------------
db1 db2 db3 db4
db5 db6 db7 db8
db9 db10 db**
===================================
Symlets sym
------------------------------
sym2 sym3 sym4 sym5
sym6 sym7 sym8 sym**
===================================
Coiflets coif
------------------------------
coif1 coif2 coif3 coif4
coif5
===================================
BiorSplines bior
------------------------------
bior1.1 bior1.3 bior1.5 bior2.2
bior2.4 bior2.6 bior2.8 bior3.1
bior3.3 bior3.5 bior3.7 bior3.9
bior4.4 bior5.5 bior6.8
===================================
ReverseBior rbio
------------------------------
rbio1.1 rbio1.3 rbio1.5 rbio2.2
rbio2.4 rbio2.6 rbio2.8 rbio3.1
rbio3.3 rbio3.5 rbio3.7 rbio3.9
rbio4.4 rbio5.5 rbio6.8
===================================
Meyer meyr
===================================
DMeyer dmey
===================================
Gaussian gaus
------------------------------
gaus1 gaus2 gaus3 gaus4
gaus5 gaus6 gaus7 gaus8
gaus**
===================================
Mexican_hat mexh
===================================
Morlet morl
===================================
Complex Gaussian cgau
------------------------------
cgau1 cgau2 cgau3 cgau4
cgau5 cgau**
===================================
Shannon shan
------------------------------
shan1-1.5 shan1-1 shan1-0.5 shan1-0.1
shan2-3 shan**
===================================
Frequency B-Spline fbsp
------------------------------
fbsp1-1-1.5 fbsp1-1-1 fbsp1-1-0.5 fbsp2-1-1
fbsp2-1-0.5 fbsp2-1-0.1 fbsp**
===================================
Complex Morlet cmor
------------------------------
cmor1-1.5 cmor1-1 cmor1-0.5 cmor1-1
cmor1-0.5 cmor1-0.1 cmor**
===================================
Doing what MATLAB does and calculating coefficients for arbitrary members of a wavelet family would be very neat. Many would require implementing a solver for the particular equation, so an optional dependency on something like SymPy would probably be necessary. If it is not available then only the predefined wavelets would be available.
Doing what MATLAB does and calculating coefficients for arbitrary members of a wavelet family would be very neat.
It can be done, but it's slow, even for Daubechies. Here's some code I found and cleaned up a bit to do exactly this for Daubechies wavelets.
However, looking at 10 Lectures on Wavelets, section 8.1.1, it looks like computing symlet coefficients is an exponential time algorithm. Does anyone know if there's an easier way to do this?
