Filter coefficients

Before doing any computations, the first step is to get the filter coefficients associated with a wavelet. The functions wavecoef and selwavlt provide access to a small database of filters. They currently know about the following wavelets:

• The standard compactly supported wavelets of Daubechies [4,5].
• Coiflets [5].
• Symmetric biorthogonal wavelets [5, p. 271].
• Family of wavelets with optimal Sobolev-regularity constructed by the author [9,10]. (The ``n<sub>z</sub>=1'' family from [10].)
• ``Beylkin 18'', see [13, p. 444].
• A filter used in speech coding constructed by Vaidyanathan and Huong [11].

The function wavecoef takes as arguments a string describing the family and a number that specifies the order of the wavelet (usually the number of coeffients in the filter). Selwavlt is menu based, instead.

        WAVECOEF -- returns some wavelet filter coefficients
        
        [h,g] = wavecoef(selection,n)
        [h1,g1,h2,g2] = wavecoef(selection,n)
        
        selection  is the name of the family:
         'Haar'       Haar's wavelet
         'Beylkin'    Only one wavelet, with 18 coefficients
         'Coiflet'    Coiflets 6, 12, 18, 24, and 30 (=n)
         'Daubechies' Her compactly supported of length n (n=2,4,...,20)  
         'Ojanen'     Most Sobolev-regular (see the documentation),
                      lengths n=8:2:40
         'Vaidyanathan'  One wavelet with 24 coefficients
         'Symmetric biorthogonal'   of orders n= 1.3, 1.5, 2.2, 2.4, 2.6, 
                      2.8, 3.3, 3.5, 3.7, and 3.9
        Output:
         h    Filter coefficients for the scaling function
         g    Coefficients for the corresponding wavelet
        
        With no input arguments returns the names of the families (the 
        biorthogonal wavelets are listed only when there are four output 
        arguments).
        
        If the user selects an orthogonal wavelet when there are four
        output arguments, h2 and g2 are copies of h and g.
        
        The first three letters are enough for  selection, which is also
        case insensitive.
        
        See also SELWAVLT, WAVDEMO.

Examples:

        [h,g] = wavecoef('dau',12)
        [h1,g1,h2,g2] = wavecoef('sym',3.7)