Wavelet Toolbox

One-Dimensional Wavelet Packet Analysis

We now turn to the Wavelet Packet 1-D tool to analyze a synthetic signal that is the sum of two linear chirps.

Starting the Wavelet Packet 1-D Tool.   

1. From the MATLAB prompt, type wavemenu.

1. The Wavelet Toolbox Main Menu appears.

   

   Click the Wavelet Packet 1-D menu item.

   The tool appears on the desktop.

   

Loading a Signal.   

2. From the File menu, choose the Load Signal option.

   

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

   

1. The sumlichr signal is loaded into the Wavelet Packet 1-D tool.

   

Analyzing a Signal.   

4. Make the appropriate settings for the analysis. Select the db2 wavelet, level 4, entropy threshold, and for the threshold parameter type 1. Click the Analyze button.

   

The available entropy types are listed below.

Type	Description
Shannon	Nonnormalized entropy involving the logarithm of the squared value of each signal sample -- or, more formally,
Threshold	The number of samples for which the absolute value of the signal exceeds a threshold .
Norm	The concentration in norm with .
Log Energy	The logarithm of "energy," defined as the sum over all samples:.
SURE (Stein's Unbiased Risk Estimate)	A threshold-based method in which the threshold equals where n is the number of samples in the signal.
User	An entropy type criterion you define in an M-file.

For more information about the available entropy types, user-defined entropy, and threshold parameters, see the wentropy reference page and Choosing the Optimal Decomposition.

Note    Many capabilities are available using the command area on the right of the Wavelet Packet 1-D window. Some of them are used in the sequel. For a more complete description, see Wavelet Packet Tool Features (1-D and 2-D).

Computing the Best Tree.   

Because there are so many ways to reconstruct the original signal from the wavelet packet decomposition tree, we select the best tree before attempting to compress the signal.

5. Click the Best Tree button.

   

1. After a pause for computation, the Wavelet Packet 1-D tool displays the best tree. Use the top and bottom sliders to spread nodes apart and pan over to particular areas of the tree, respectively.

   Observe that, for this analysis, the best tree and the initial tree are almost the same. One branch at the far right of the tree was eliminated.

   

About Wavelet Packet Analysis

Compressing a Signal Using Wavelet Packets

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