Wavelet Toolbox

Example 1

Let us take the example of Binlets proposed by Strang and Nguyen in the pages 216-217 of the book Wavelets and Filter Banks (See [StrN96] in References).

Note    The M-files used in this example can be found in the wavedemo directory.

The full family name is: Binlets.

The short name of the wavelet family is: binl.

The wavelet type is: 2 (Biorthogonal with FIR filters).

The order of the wavelet within the family is: 7.9 (we just use one in this example).

The M-file used to generate the filters is binlwavf.m

Then to add the new wavelet, type:

% Add new family of biorthogonal wavelets. 
     wavemngr('add','Binlets','binl',2,'7.9','binlwavf')

% List wavelets families.
     wavemngr('read')

ans =

=================================== 
Haar                haar           
Daubechies          db             
Symlets             sym            
Coiflets            coif           
BiorSplines         bior           
ReverseBior         rbio           
Meyer               meyr           
DMeyer              dmey           
Gaussian            gaus           
Mexican_hat         mexh           
Morlet              morl           
Complex Gaussian    cgau           
Shannon             shan           
Frequency B-Spline  fbsp           
Complex Morlet      cmor 
Binlets             binl 
===================================

If you want to get online information on this new family, you can build an associated help file which would look like:

function binlinfo
%BINLINFO Information on biorthogonal wavelets (binlets).
%
%   Biorthogonal Wavelets (Binlets)
%
%   Family                  Binlets
%   Short name              binl
%   Order Nr,Nd             Nr = 7 , Nd = 9
%
%   Orthogonal              no
%   Biorthogonal            yes
%   Compact support         yes
%   DWT                     possible
%   CWT                     possible
%
%   binl Nr.Nd              ld                      lr      
%                      effective length        effective length
%                        of LoF_D                of HiF_D
%   binl 7.9                 7                       9

The associated M-file to generate the filters (binlwavf.m) is:

function [Rf,Df] = binlwavf(wname)
%BINLWAVF Biorthogonal wavelet filters (Binlets).
%   [RF,DF] = BINLWAVF(W) returns two scaling filters
%   associated with the biorthogonal wavelet specified
%   by the string W.
%   W = 'binlNr.Nd' where possible values for Nr and Nd are:
               Nr = 7  Nd = 9
%   The output arguments are filters:
%           RF is the reconstruction filter
%           DF is the decomposition filter

% Check arguments.
if errargn('binlwavf',nargin,[0 1],nargout,[0:2]), error('*'); 
end
% suppress the following line for extension
Nr = 7; Nd = 9;

% for possible extension
% more wavelets in 'Binlets' family
%----------------------------------
if nargin==0
    Nr = 7; Nd = 9;
elseif  isempty(wname)
    Nr = 7; Nd = 9;
else
    if ischar(wname)
        lw = length(wname);
        ab = abs(wname);
        ind = find(ab==46 | 47<ab | ab<58);
        li = length(ind);
        err = 0;
        if      li==0
            err = 1;
        elseif  ind(1)~=ind(li)-li+1
            err = 1;
        end 
        if err==0 , 
            wname = str2num(wname(ind));
            if isempty(wname) , err = 1; end
        end
    end     
    if err==0
        Nr = fix(wname); Nd = 10*(wname-Nr);
    else
        Nr = 0; Nd = 0;
    end
end

% suppress the following lines for extension
% and add a test for errors.
%-------------------------------------------
if Nr~=7 , Nr = 7; end
if Nd~=9 , Nd = 9; end

if Nr == 7
   if Nd == 9
      Rf = [-1 0 9 16 9 0 -1]/32;
      Df = [ 1 0 -8 16 46 16 -8 0 1]/64;
   end
end

Adding a New Wavelet Family

Example 2