liftwave (Wavelet Toolbox)

Lifting schemes

Syntax

LS = liftwave(WNAME)
LS = liftwave(WNAME,'Int2Int')

Description

LS = liftwave(WNAME) returns the lifting scheme associated with the wavelet specified by WNAME. LS is a structure, not an integer, and used by lwt, ilwt, lwt2, etc.

LS = liftwave(WNAME,'Int2Int') performs an integer to integer wavelet transform. Using 'Int2Int' produces an LS such that when you use [CA,CD] = lwt(X,LS) or Y = lwt(X,LS) and X is a vector of integers, the resulting CA, CD, and Y are vectors of integers. If you omit 'Int2Int' then lwt produces vectors of real numbers.

The valid values for WNAME are

WNAME Values
Comments

'lazy'
A "lazy" wavelet is a second-generation wavelet and is not a true mathematical wavelet.

'haar'
same as 'db1', 'bior1.1', and cdf1.1'

'db1', 'db2', 'db3', 'db4', 'db5', 'db6', 'db7', 'db8'
'db2' same as'sym2', 'db3', and 'sym4'

'sym2', 'sym3', 'sym4', 'sym5', 'sym6', 'sym7', 'sym8'

Cohen-Daubechies-Feauveau wavelets

'cdf1.1','cdf1.3','cdf1.5'
'cdf3.1','cdf3.3','cdf3.5'
'cdf5.1','cdf5.3','cdf5.5'

'cdf2.2','cdf2.4','cdf2.6' 'cdf4.2','cdf4.4','cdf4.6' 'cdf6.2','cdf6.4','cdf6.6'
cdfX.Y' same as 'biorX.Y' except for bior4.4 and bior5.5.

'biorX.Y'
See waveinfo

'rbioX.Y'

reverse of 'biorX.Y'.
See waveinfo

'bs3'
same as 'cdf4.2'

'rbs3'
reverse of 'bs3'

'9.7'
same as 'bior4.4'

'r9.7'
reverse of '9.7'

WNAME Values	Comments
'lazy'	A "lazy" wavelet is a second-generation wavelet and is not a true mathematical wavelet.
'haar'	same as 'db1', 'bior1.1', and cdf1.1'
'db1', 'db2', 'db3', 'db4', 'db5', 'db6', 'db7', 'db8'	'db2' same as'sym2', 'db3', and 'sym4'
'sym2', 'sym3', 'sym4', 'sym5', 'sym6', 'sym7', 'sym8'
Cohen-Daubechies-Feauveau wavelets 'cdf1.1','cdf1.3','cdf1.5' 'cdf3.1','cdf3.3','cdf3.5' 'cdf5.1','cdf5.3','cdf5.5' `'cdf2.2','cdf2.4','cdf2.6' 'cdf4.2','cdf4.4','cdf4.6' 'cdf6.2','cdf6.4','cdf6.6'`	cdfX.Y' same as 'biorX.Y' except for bior4.4 and bior5.5.
'biorX.Y'	See waveinfo
'rbioX.Y'	reverse of 'biorX.Y'. See waveinfo
'bs3'	same as 'cdf4.2'
'rbs3'	reverse of 'bs3'
'9.7'	same as 'bior4.4'
'r9.7'	reverse of '9.7'

For more information about lifting schemes, see lsinfo.

Examples

% Start from the db2 wavelet and get the
% corresponding lifting scheme.
lsdb2 = liftwave('db2');

% Visualize the obtained lifting scheme.
displs(lsdb2);

lsdb2 = {...                                         
'd'             [ -1.73205081]              [0]   
'p'             [ -0.06698730  0.43301270]  [1]   
'd'             [  1.00000000]              [-1]  
[  1.93185165]  [  0.51763809]              []    
};

See Also
laurpoly

liftfilt ls2filt