Supported 2-D CWT wavelets and Fourier transforms
cwtftinfo2
lists the supported 2-D continuous
wavelet transform (CWT) wavelets and corresponding parameters for
use with cwtft2
.
cwtftinfo2
CWTFTINFO2 Information on wavelets for CWTFT2 CWTFTINFO2 provides information on the available wavelets for 2-D Continuous Wavelet Transform using FFT. The wavelets are defined by their Fourier transform. The formulae giving the Fourier transform of the wavelet which short name (see below) is SNAME will be displayed using CWTFTINFO2(SNAME). The table below gives the short name of each wavelet and the associated parameters: first, the name of parameter and then the default value. WAV_Param_Table = {... 'morl' , defaults: omega0 = 6; sigma = 1; epsilon = 1; 'mexh' , defaults: p = 2; sigmax = 1; sigmay = 1; 'paul' , defaults: p = 4; 'dog' , defaults: alpha = 2; 'cauchy' , defaults: alpha = pi/6; sigma = 1; L = 4; M = 4; 'escauchy' , defaults: alpha = pi/6; sigma = 1; L = 4; M = 4; 'gaus' , defaults: p = 1; sigmax = 1; sigmay = 1; 'wheel' , defaults: sigma = 2; 'fan' , defaults: omega0 = 5.336; sigma = 1; epsilon = 1; J = 6.5; 'pethat' , defaults: No parameters. 'dogpow' , defaults: alpha = 1.25; p = 2; 'esmorl' , defaults: omega0 = 6; sigma = 1; epsilon = 1; 'esmexh' defaults: sigma = 1; epsilon = 0.5; 'gaus2' , defaults: p = 1; sigmax = 1; sigmay = 1; 'gaus3' , defaults: A = 1; B = 1; p = 1; sigmax = 1; sigmay = 1; 'isodog' , defaults: alpha = 1.25; 'dog2' , defaults = alpha = 1.25; 'isomorl' , defaults: omega0 = 6; sigma = 1; 'rmorl' , defaults: omega0 = 6; sigma = 1; epsilon = 1; 'endstop1' , defaults: omega0 = 6; 'endstop2' , defaults: omega0 = 6; sigma = 1; 'gabmexh' , defaults: omega0 = 5.336; epsilon = 1; 'sinc' , defaults: Ax = 1; Ay = 1; p = 1; omega0X= 0; Omega0Y = 0; }; The various wavelets may be grouped in families as follow: MORLET: 'morl' , 'esmorl' , 'rmorl' , 'isomorl' DOG: 'dog' , 'isodog' , 'dog2' , 'dogpow' GAUSS: 'mexh' , 'gaus' , 'gaus2' , 'gaus3' , 'esmexh' PAUL: 'paul' CAUCHY: 'cauchy' , 'escauchy' WHEEL: 'wheel', 'pethat' MISCELLANEOUS : 'endstop1' , 'endstop2' , 'gabmexh' , 'sinc' , 'fan' REFERENCES Two-Dimensional Wavelets and their Relatives J.-P. Antoine, R. Murenzi, P. Vandergheynst andS. Twareque Ali Cambridge University Press - 2004 Two-dimensional wavelet transform profilometry Fringe Pattern Analysis Using Wavelet Liverpool John Moores University http://www.ljmu.ac.uk See also CWTFT2
Display the expression for the 2-D Fourier transform of the Cauchy wavelet. After displaying the Fourier transform for any wavelet, you can use the drop-down list in the bottom left to view the Fourier transform for any supported wavelet.
cwtftinfo2('cauchy')
wname
— Wavelet nameWavelet name, specified as a character vector or string scalar. The following table lists the supported wavelets for the 2-D CWT and associated parameters:
Wavelet name | Parameters |
---|---|
'morl' | {'Omega0',6;'Sigma',1;'Epsilon',1} |
'mexh' | {'p',2;'sigmax',1;'sigmay',1} |
'paul' | {'p',4} |
'dog' | {'alpha',1.25} |
'cauchy' | {'alpha','pi/6';'sigma',1;'L',4;'M',4} |
'escauchy' | {'alpha','pi/6';'sigma',1;'L',4;'M',4} |
'gaus' | {'p',1;'sigmax',1;'sigmay',1} |
'wheel' | {'sigma',2} |
'fan' | {'Omega0X',5.336;'Sigma',1;'Epsilon',1;'J',6.5} |
'pethat' | None |
'dogpow' | {'alpha',1.25;'p',2} |
'esmorl' | {'Omega0',6;'Sigma',1;'Epsilon',1} |
'esmexh' | {'Sigma',1;'Epsilon',0.5} |
'gaus2' | {'p',1;'sigmax',1;'sigmay',1} |
'gaus3' | {'A',1;'B',1;'p',1;'sigmax',1;'sigmay',1} |
'isodog' | {'alpha',1.25} |
'dog2' | {'alpha',1.25} |
'isomorl' | {'Omega0',6;'Sigma',1} |
'rmorl' | {'Omega0',6;'Sigma',1;'Epsilon',1} |
'endstop1' | {'Omega0',6} |
'endstop2' | {'Omega0',6;'Sigma',1} |
'gabmexh' | {'Omega0',5.336;'Epsilon',1} |
'sinc' | {'Ax',1;'Ay',1;'p',1;'Omega0X',0;'Omega0Y',0} |
Example: cwtftinfo2('paul')
Data Types: char
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