DE OLIVEIRA WAVELETS  2003 (DE OLIVEIRA ONDELETTES)

By Hélio M. de Oliveira and Luciana R. Soares  {hmo,lusoares}@ufpe.br

Here you will find instructions for installing deOliveira & Complex deOliveira wavelets in the MATLAB wavelet toolbox.
Matlab version must be > 6.x

Wavelet Information:
            full name             -      de Oliveira
            compact name    -      deoalpha      (e.g. deo0.08333)
            parameter alpha  -      alpha = 0.00000  0.08333  0.16666  0.25000  0.33333
                                            0 <= alpha <= 1/3
Complex version

            full name             -      de Oliveira
            compact name    -      cdeoalpha
            parameter alpha  -      alpha = 0.00000  0.08333  0.16666  0.25000  0.33333
                                            0 <= alpha <= 1/3
 
In the Matlab wavelet toolbox, there exist five kinds of wavelets (type the command waveinfo on the prompt):
(i) crude wavelets (ii) Infinitely regular wavelets (iii) Orthogonal and compactly supported wavelets
(iv) biorthogonal and compactly supported wavelet pairs and (v) complex wavelets.

Complex wavelets present as a rule interesting symmetry and possess closed expression.
In contrast with standard continuous complex wavelets (cgauN Gaussian, cmorFb-Fc Morlet,
Shannon shanFb-Fc, fbspM-Fb-Fc frequency B-spline), the "de Oliveira" scaling function do exist
and de Oliveira wavelets are orthogonal so the reconstruction property is insured.
To deal with such trouble, two de Oliveira wavelets can de added to the wavelet toolbox:

cdeo is the complex version of de Oliveira (type 5), but the orthogonality is not exploited.
deo is an orthogonal infinitely regular de Oliveira (type 3), but often they are not assumed to be complex.

Algorithm:

STEP 1 - Download the m files     |  deowavf.m  |  deoinfo.m  |    also   |   cdeowavf.m  |  cdeoinfo.m  |
                Files must be saved as .m

STEP 2 - Place the above files at the folder MatLab/toolbox/wavelet/wavelet
              If your Matlab version has not such a path, you can find other similar wavelet files as "dbwavf.m"
              and place "deowavf.m" and "deoinfo.m" at the same place.

STEP 3 - In order to install de Oliveira wavelet, type the following at the Matlab Command prompt:

           wavemngr('add','de Oliveira','deo',3,'0 0.08333 0.16666 0.25000 0.33333','deowavf',[-12,12])
           wavemngr('add','de Oliveira','cdeo',5,'0 0.08333 0.16666 0.25000 0.33333','cdeowavf',[-12,12])
This will install "type 3" and "type 5" wavelets

1) To check whether de Oliveira was successfully installed or not, type at the prompt of the MatLab Command Window :  wavemngr('read',1)

2) To see de Oliveira wavelet information. Type at the prompt of the MatLab Command Window :
type deoinfo or cdeoinfo

3) Now type wavemenu 
 

Matlab m file for computing CWT

% typical deo computation
% load a signal (e.g. cuspamax, nelec, lelecum etc.)
 load cuspamax;
 dados = cuspamax(1:1024);
 lv = length(dados);
 subplot(311), plot(dados); title('signal...');
% performing a cwt by deo0.33333
% all integer scales from 1 to 64
 subplot(313)
 wt = cwt(dados,1:64,'deo0.33333','plot');
 title('CWT, absolute coefficients')
 colormap(bone(64));
 ylabel('scale');

Final Remarks:

DE OLIVEIRA

Reference:

[1] DE OLIVEIRA, H.M., SOARES, L.R., FALK, T.H., A Family of Wavelets and a New Orthogonal Multiresolution Analysis Based on the Nyquist Criterion,
Proc. IEEE/SBrT Int. Telecomm. Symp.
, 2002. pp. 384-389. (selected paper for special issue) 

[2]  DE OLIVEIRA, H.M., SOARES, L.R., FALK T.H., A Family of Wavelets and a New Orthogonal Multiresolution Analysis Based on the Nyquist Criterion ,  [.pdf]
Journal of Communication and Information Systems,
Campinas, SP: ,
v.18, n.1, vol.18, N.1, June 2003, ISSN 1980-6604.