afwt   

 afwt.m

 Adjoint of Forward Fast wavelet transform.

 Usage: x = afwt(w, h0, h1, J, sym);
 w - nx1 wavelet transoform vector
 h0 - lowpass decomposition filter
 h1 - highpass decomposition filter
      h0 and h1 should be zero padded appropriately so that they have the
      same length, and this length is even.
 J - number of levels in the filter bank.
 
 sym - How to extend the input. (currently using only sym=1)
     sym=0: periodization
     sym=1: type-I symmetric extension ( [... x(2) x(1) x(2) x(3) ...])
            The wavelet filters must have type-I even symmetry 
            (e.g. daub79)
     sym=2: type-II symmetric extension ( [... x(2) x(1) x(1) x(2) x(3) ...])
            The lowpass filter must have type-II even symmetry, 
            The highpass filter must have type-II odd symmetry.
            (e.g. daub1018)

 A friendly way to understand/implement symmetric wavelets and adjoints 
 is to treat symmetric extension and filtering as two separate operations. 

 Written by: M. Salman Asif
 Created: December 2007

0001 % afwt.m
0002 %
0003 % Adjoint of Forward Fast wavelet transform.
0004 %
0005 % Usage: x = afwt(w, h0, h1, J, sym);
0006 % w - nx1 wavelet transoform vector
0007 % h0 - lowpass decomposition filter
0008 % h1 - highpass decomposition filter
0009 %      h0 and h1 should be zero padded appropriately so that they have the
0010 %      same length, and this length is even.
0011 % J - number of levels in the filter bank.
0012 %
0013 % sym - How to extend the input. (currently using only sym=1)
0014 %     sym=0: periodization
0015 %     sym=1: type-I symmetric extension ( [... x(2) x(1) x(2) x(3) ...])
0016 %            The wavelet filters must have type-I even symmetry
0017 %            (e.g. daub79)
0018 %     sym=2: type-II symmetric extension ( [... x(2) x(1) x(1) x(2) x(3) ...])
0019 %            The lowpass filter must have type-II even symmetry,
0020 %            The highpass filter must have type-II odd symmetry.
0021 %            (e.g. daub1018)
0022 %
0023 % A friendly way to understand/implement symmetric wavelets and adjoints
0024 % is to treat symmetric extension and filtering as two separate operations.
0025 %
0026 % Written by: M. Salman Asif
0027 % Created: December 2007
0028