Wavelet Toolbox

New Wavelet for CWT Using the Graphical Interface

1. Start the New Wavelet for CWT Tool.

1. From the MATLAB prompt, type

   • wavemenu
     

   The Wavelet Toolbox Main Menu appears. Click the New Wavelet for CWT menu item to display the Pattern Adapted Admissible Wavelet Design Tool.

   

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2. Load the original pattern.

1. The MAT-file defining the pattern can contain more than one variable. In that case, the variable Y is considered if it exists; otherwise, the first variable is considered.

3. From the File menu, choose the Load Pattern option.

1. When the Load Pattern dialog box appears, select the demo MAT-file ptpssin1.mat, which should reside in the MATLAB directory toolbox/wavelet/wavedemo. Click the OK button.

   

   The selected pattern denoted by F is defined on the interval [0,1] and is of integral 0.1592. It is not a wavelet, but it is a good candidate because it oscillates like a wavelet.

4. Perform pattern approximation.

1. Accept the default parameters leading to use a polynomial of degree 3 with constraints of continuity at the borders 0 and 1, to approximate the pattern F. Click the Approximate button.

   After a pause for computation, the tool displays the new wavelet in green superimposed with the original pattern in red.

   

   The result is not really satisfactory. A solution is to increase the polynomial degree to fit better the pattern.

5. Using the Polynomial Degree menu, increase the degree by selecting 6. Then click the Approximate button again.

   

1. The result is now of good quality and can be used for pattern detection.

6. Pattern detection using the new wavelet.

1. Click the Run button.

   After a pause for computation, the tool displays the running signal and the pattern detection by CWT using the adapted wavelet.

   

   The running signal is the superimposition of two dilated and translated versions of the pattern F, namely F((t-20)/8) and F((t-40)/4). The two pairs (position, scale) to be detected are given by (20,8) and (40,4) and are materialized by dashed lines in the lower right graph of the contour plot of the CWT. The detection is perfect because the two local maxima of the absolute values of the continuous wavelet coefficients fit perfectly.

7. Using the Running signal frame, select the Noise check box to add an additive noise to the previous signal. Click the Run button again.

   

1. The quality of the detection is not altered at all.

8. Compare the adapted wavelet and well-known wavelets.

1. Let us now compare the performance for pattern detection of the adapted wavelet versus well-known wavelets. Click the Compare button. A new window appears.

   

   This tool displays the pattern detection performed with the adapted wavelet on the left and db1 wavelet (default) on the right. The two positions are perfectly detected in both cases but scales are slightly underestimated by the db1 wavelet.

   The tool allows you to generate various running signals and choose the wavelet to be compared with the adapted one.

   Click the Close button to get back to the main window.

New Wavelet for CWT Using the Command Line

Saving the New Wavelet

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