Wavelet Toolbox

New Wavelet for CWT Using the Command Line

The following example illustrates how to generate a new wavelet starting from a pattern.

• % Load original pattern: a pseudo sine one.
  load ptpssin1; 
  
  % Variables X and Y contain the pattern.
  whos
  
    Name          Size                   Bytes  Class
  
    IntVAL        1x1                        8  double array
    X             1x256                   2048  double array
    Y             1x256                   2048  double array
    caption       1x35                      70  char array
  
  Grand total is 548 elements using 4174 bytes
  
  % This example is a demo-example, so we have the value of the
  % integral of the pattern as well as the details about its
  % construction in the caption variable.
  
  IntVAL
  
  IntVAL =
  
      0.1592
  
  % The pattern defined on the interval [0,1] is of integral 0.1592. 
  % So it is not a wavelet but it is a good candidate since it 
  % oscillates like a wavelet.
  plot(X,Y), title('Original Pattern')
  
  % To synthesize a new wavelet adapted to the given pattern, let
  % us use a least squares polynomial approximation of degree 6 with
  % constraints of continuity at the beginning and the end of the
  % pattern.
  [psi,xval,nc] = pat2cwav(Y, 'polynomial',6, 'continuous') ;
  
  % The new wavelet is given by xval and nc*psi.
  plot(X,Y,'-',xval,nc*psi,'--'), 
  title('Original Pattern and Adapted Wavelet (dashed line)')
  
  
  % Let us notice that the version of the wavelet correctly 
  % defined in order to be used in the CWT algorithm must be of
  % square norm equal to 1. It is simply given by xval and psi.
  

New Wavelet for CWT

New Wavelet for CWT Using the Graphical Interface

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