Wavelet Toolbox

Example 1

Let us take the example of Binlets proposed by Strang and Nguyen in 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 the following:

• 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

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