Wavelet Power Spectrum

The wavelet transform converts the data array into a series of wavelet coefficients, each of which represents the amplitude of the wavelet function at a particular location within the array and for a particular wavelet scale.

The Wavelet Power Spectrum viewer, shown in the following figure, allows you to visualize the wavelet power as a three-dimensional surface plot, where the height of the surface represents the magnitude of the wavelet coefficients.

Figure 2-3: The Wavelet Power Spectrum 3D viewer.

File Menu

Open State...

This menu item opens a previously saved "state" file into a new window.

Save State...

This menu item saves the current state of the Wavelet Power Spectrum into a file.

Export To...

Bitmap File [Windows only]: The bitmap file saves the current image as a bitmap.

Vector Metafile [Windows only]: The vector metafile produces a scalable image file, but may not be able to accurately reproduce the 3D geometry.

Bitmap Pict [Macintosh only]: The bitmap pict saves the current image as a bitmap.

Bitmap Postscript: The bitmap postscript format saves the current image as a bitmap.

Vector Postscript: The vector postscript format takes less disk space than bitmap, and is scalable, but may not be able to accurately reproduce the 3D geometry.

VRML: The Virtual Reality Markup Language produces a three-dimensional output file suitable for web publication.

Note
It is not always possible to translate the complicated 3D geometry produced by IDL object graphics into equivalent VRML code.

Print

This menu item will output the image to a printer.

Close

This menu item closes the Wavelet Power Spectrum viewer.

Edit Menu

Undo

This menu item will undo the previous rotation, scaling, or translation of the model.

Copy To Clipboard

This menu item makes a copy of the current graphics image and places it on the system clipboard.

View Menu

Color Table

Selecting this item brings up the XLOADCT color table editor. You can then choose different color tables for the graphics image. See "XLOADCT" (IDL Reference Guide) for more information.

Drag Quality

This submenu has three different settings that affect the drawing speed during object manipulations:

Low— only the axes are exposed for graphics manipulation such as rotation and translation;

Medium— low resolution graphics are used for graphics manipulation;

High— full resolution is used for all graphics manipulations

Wavelet Options

If you select this menu item, the Wavelet Options panel will be hidden. Select this menu item again to show the panel.

View Options

If you select this menu item, the View Options panel will be hidden. Select this menu item again to show the panel.

Help Menu

This menu contains Help items for the Wavelet Power Spectrum and for IDL.

Wavelet Options

You can change the current wavelet family or the order. The plot will be automatically updated.

Note
For two-dimensional input data, only the discrete wavelet functions are available.

View Options

3D

Turn this button off to rotate the image so it appears flat. Turn this button on to rotate the image to a three-dimensional perspective. For vector data, this button also controls whether the data series and global wavelet plot are flat or vertical.

Note
The surface will remain three-dimensional; only the viewpoint is changed.

Color Bar

Turn this button off to remove the color bar at the bottom. Turn this button on to restore the color bar.

Data Plot [One-dimensional only]

Turn this button off to remove the data series plot at the back. Turn this button on to restore the plot.

Global [One-dimensional only]

Turn this button off to remove the plot of the global wavelet. Turn the button on to restore the plot.

Zero Phase Lines [Complex wavelet functions only]

Turn this button on to add the zero wavelet phase lines to the surface plot.

Energy Scaling

These buttons control the scaling of the wavelet magnitude in the Z-direction.

Power

The power is the absolute-value-squared of the wavelet coefficients. The height of each point measures the contribution to the total energy.

This scaling emphasizes large peaks and sharp discontinuities, and de-emphasizes low-amplitude background noise.

Magnitude

The magnitude is the absolute value of the wavelet coefficients, and provides a measure of the relative amplitude of each point.

This scaling reduces the weighting given to large peaks and can bring out finer-detail features.

Decibels

The power can also be displayed in decibels, normalized relative to the mean of the wavelet power spectrum.

Since decibels are a logarithmic scale, the smallest wavelet coefficients are given just as much weight as the largest coefficients. This scaling is most useful for data that contain a broad range of energy, or that contain a single sharp spike embedded in small-amplitude noise.

db Cutoff

You can specify the lower cutoff for the Decibel plot. The default is –50 db.

Surface Style

There are seven different surface plots from which to choose:

Points— places colored dots at each location/height;

Mesh— creates an unfilled surface plot;

Surface— creates a shaded filled surface;

XZ Lines— draws lines parallel to the X-axis, one for each Y location;

YZ Lines— draws lines parallel to the Y-axis, one for each X location;

Lego— draws a lego-block plot with mesh sides;

Lego filled— draws a lego-block plot with solid sides.

You can also use the buttons to remove or add a "Skirt" around the surface, make the surface "Flat", or change to a "Gray" palette.

Contour Lines

You can choose to include contour lines at the top of the plot, the bottom, or three dimensional.

Color Contours

You can also put color contours at the top, bottom, or 3D. The color contours can be either open or filled. The color palette is the same as that used for the surface plot.

Tip
To produce a shaded surface with contours, make the surface "Shaded", set the "Gray" button, and select "3D" color contours.

Significance

The statistical significance of each point in the wavelet power spectrum can be plotted as a three-dimensional sheet, or as contours on the top, bottom, or 3D. Points in the wavelet power spectrum that lie above the sheet (or within the contours) are said to be "significant at the xx% level," where xx is your chosen percentage. You can choose the significance level as 10%, 5%, 1%, or 0.1%.

Note
The significance level is given by the chi-square function with one degree of freedom for real wavelet functions, or two degrees of freedom for complex wavelets (such as the Morlet). This significance is relative to the wavelet power spectrum of a random dataset (assuming Gaussian "white noise").

Power Display

The graphics window contains the three-dimensional image and a color palette.

If you move the mouse cursor over points in the image, the current location and power will be displayed in the Status Bar.

Rotation, Translation, Stretching

To rotate the image, click on the image while holding down the left mouse button, and drag the mouse pointer to rotate the image about the midpoint.

To translate the image, click on the image while holding down the right mouse button (on the Macintosh hold down the command key also), and drag the mouse pointer.

To stretch the image, click on the image while holding the middle mouse button (on Windows hold down the Ctrl key also; on Macintosh hold down the Option key). Drag the mouse pointer right/left to stretch/shrink in the X-direction, drag the pointer up/down to stretch/shrink in the Y-direction.