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Tools for visualization

The heart of the wavelet packet programs is showwp, which allows all of the above operations (selecting bases, setting cost functions, etc.) and many others to be performed interactively. An example (from the demo wpsig) is shown in figure 7, where a sinusoid with noise is analyzed. The top part is a tree as in figure 5, the blocks with red boundaries are those selected in the basis. The lower half of the figure is a phaseplane plot (frequency against time with amplitude shown in different shades of gray) generated by phasepln. Note how the wavelet packets recognize the frequency of the sinusoid by concentrating most of the wavelet packet coefficients to the two black horizontal bands.


  
Figure 7: showwp and wpsig
pict/window/gif/web/dither/wpsigc.gif

        SHOWWP -- shows wavelet packet coefficients and many other things
        
        showwp(w, h, g)
        showwp(w, f, h, g)
        
        Displays the tree of the wavelet packet coefficients in w. f is
        the original vector (possibly an empty vector). If any selections
        are made, the selected packets are made to stand out. Both f and
        selection are optional.
        
        The display is divided into two parts: in the top part is the tree
        of the wavelet packet coefficients, the bottom part is used for
        graphing other things.
        
        The original vector is the very first row of the tree. Here white
        means large values, black small (possibly) negative values.
        
        The wavelet packet coefficients form the rest of tree. The left
        branches are the result of convolution-decimation with the low
        pass filter (scaling function), right branches with the high pass
        filter (wavelet). Here only the absolute values of the
        coefficients are drawn: white means large absolute value, black
        means zero.
        
        Clicking in a box on the first row shows the original vector,
        clicking in any other box shows the graph of the wavelet packet
        corresponding to that box.
        
        Select menu:
            Packet          toggle the selected/unselected state of a 
                            single packet
            Group           toggle the selected/unselected state of a box
            Fixed level     click anywhere in the tree to select a level
            Wavelet basis   selects the wavelet basis
            Best level      selects the level with lowest cost
            Best basis      selects the basis with lowest cost
            Clear           clears all selections
        
        Action menu:
            Inverse transform    computes the inverse transform using 
                                 current selection
            Phaseplane plot      displays the phaseplane plot for the 
                                 currently selected basis
            Nonincreasing rearrengement
                                 displays the nonincreasing rearrengement
                                 of the wavelet packet coefficients
            Compute cost         displays the cost of various things
        
        Discard menu:
            Discards all coefficients whose absolute value is less than the
            selected percentage of the L2-norm of the whole collection of 
            wavelet packet coefficients.
        
        Options menu:    
            Set cost function      allows to select the cost function
            Show cost function     shows which cost function is being used
            Natural order          switches the display to natural order
            Sequency order         switches the display to sequency order
            --> Color              switches the display to color
            --> B/W                switches the display to black and white
        
        See also PHASEPLN, WMENU, WPDEMO, WPA1, WPS1, BESTBASE, BESTLEVL, 
                 FIXLEVEL, WAVBASIS.



Harri Ojanen
1998-05-02