Wavelet Toolbox™

Real or complex continuous 1-D wavelet coefficients using extension parameters

Syntax

• COEFS = cwtext(S,SCALES,'wname')
  COEFS = cwtext(S,SCALES,'wname',PropName1,ProVal1, ...)
  

Description

COEFS = cwtext(S,SCALES,'wname') computes the continuous wavelet coefficients of the vector S at real, positive SCALES, using a wavelet named 'wname'. The signal S is real; the wavelet can be real or complex.

COEFS = cwtext(S,SCALES,'wname',PropName1,ProVal1, ...) computes and plots the continuous wavelet transform coefficients using extra parameters. Valid values for PropName are:

• 'ExtMode'
• 'ExtSide'
• 'ExtLen'
• 'PlotMode'
• 'xlim'

The continuous wavelet transform coefficients are computed using the extension parameters:

• 'ExtMode'
• 'ExtSide'
• 'ExtLen'

Valid values for ExtMode are:

• 'zpd' (zero padding)
• 'sp0' (smooth extension of order 0)
• 'sp1' (smooth extension of order 1)

etc.

Valid values for ExtSide are:

• ExtSide = 'l' (or 'u') for left (or up) extension
• ExtSide = 'r' (or 'd') for right (or down) extension
• ExtSide = 'b' for extension on both sides
• ExtSide = 'n' null extension

For the complete list of valid values for ExtMode and ExtSide, see wextend.

ExtLen is the length of extension.

Default values for extension parameters are 'zpd' and 'b'. ExtLen is computed using the maximum of SCALES.

Instead of three parameters, use the following syntaxes:

• EXTMODE = struct('Mode',ModeVAL,'Side',SideVAL,'Len',LenVAL);

  EXTMODE = {ModeVAL,SideVAL,LenVAL};

COEFS = cwtext(...,'PlotMode',PLOTMODE) computes and plots the continuous wavelet transform coefficients. Coefficients are colored using PLOTMODE:

• PLOTMODE = 'lvl' (By scale)
• PLOTMODE = 'glb' (All scales)
• PLOTMODE = 'abslvl' or 'lvlabs' (Absolute value and By scale)
• PLOTMODE = 'absglb' or 'glbabs' (Absolute value and All scales)

You get 3-D plots (surfaces) using the same keywords listed above for the PLOTMODE parameter, preceded by '3D', for example, PLOTMODE = '3Dlvl'.

When PLOTMODE = 'scal' or 'scalCNT' the continuous wavelet transform coefficients and the corresponding scalogram (percentage of energy for each coefficient) are computed.

When PLOTMODE is 'scal', a scaled image of scalogram is displayed. When PLOTMODE is 'scalCNT', a contour representation of scalogram is displayed.

If the XLIM parameter is given, the continuous wavelet transform coefficients are colored using PLOTMODE and XLIM.

XLIM = [x1 x2] with 1 <= x1 < x2 <= length(S).

For each given scale a within the vector SCALES, the wavelet coefficients C(a,b) are computed for b = 1 to ls = length(S), and are stored in COEFS(i,:) if a = SCALES(i).

Output argument COEFS is a la-by-ls matrix where la is the length of SCALES. COEFS is a real or complex matrix depending on the wavelet type.

Examples of valid use are as follows:

• t = linspace(-1,1,512);
  s = 1-abs(t);
  c = cwtext(s,1:32,'cgau4');
  c = cwtext(s,[64 32 16:-2:2],'morl');
  c = cwtext(s,[3 18 12.9 7 1.5],'db2');
  c = cwtext(s,1:32,'sym2','plotMode','lvl');
  c = cwtext(s,1:64,'sym4','plotMode','abslvl','xlim',[100 400]);
  
  [c,Sc] = cwtext(s,1:64,'sym4','plotMode','scal');
  [c,Sc] = cwtext(s,1:64,'sym4','plotMode','scalCNT');
  [c,Sc] = cwtext(s,1:64,'sym4','plotMode','scalCNT', ...
                                'extMode','sp1');
  
  c = cwtext(s,1:64,'sym4','plotMode','lvl','extMode','sp0');
  c = cwtext(s,1:64,'sym4','plotMode','lvl','extMode','sp1');
  c = cwtext(s,1:64,'sym4','plotMode','lvl', ...
                           'extMode',{'sp1','b',300});
  
  ext = struct('Mode','sp1','Side','b','Len',300);
  c = cwtext(s,1:64,'sym4','plotMode','lvl','extMode',ext);
  

Examples

This example demonstrates the difference between a continuous wavelet transform which deals with signal extension and one which does not.

• % Load and plot the signal
  load wcantor
  plot(wcantor)
  
  % Compute and plot the coefficients
  cwt(wcantor,(1:256),'mexh','absglb');
  colormap(pink(4))
  
  

In this figure above, which is produced by the cwt function, the values of coefficients are tremendously affected by the boundary effect due to the discontinuity of the signal on the right. The default (zero-padding) extension mode on the right explains this important discontinuity because the last value is 1. On the left there is no effect because the first value is 0.

• % Compute and plot the coefficients with adapted extension mode
  figure;
  cwtext(wcantor,(1:256),'mexh','extmode','sp0','extLen',2000, ...
                                'plotMode','absglb');
  colormap(pink(4))
  

In this figure, produced by the cwtext function, the suitable extension mode of the signal is very efficient, giving as it can be seen, a good result.

See Also
cwt, wavedec, wavefun, waveinfo, wcodemat

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