This section takes you through the features of complex continuous wavelet analysis using the Wavelet Toolbox™ software and focuses on the differences between the real and complex continuous analysis.

You can refer to the section Command Line Continuous Wavelet Analysis if you want to learn how to

Zoom in on detail

Display coefficients in normal or absolute mode

Choose the scales at which the analysis is performed

Switch from scale to pseudo-frequency information

Exchange signal and coefficient information between the disk and the graphical tools

Wavelet Toolbox software requires only one function for
complex continuous wavelet analysis of a real valued signal: `cwt`

. You'll find full information about
this function in its reference page.

In this section, you'll learn how to

Load a signal

Perform a complex continuous wavelet transform of a signal

Produce plots of the coefficients

Since you can perform analyses either from the command line or using the graphical interface tools, this section has subsections covering each method.

This example involves a cusp signal.

Load a signal.

From the MATLAB

^{®}prompt, typeload cuspamax;

You now have the signal

`cuspamax`

in your workspace:whos

Name Size Bytes Class `caption`

`1x71`

`142`

`char array`

`cuspamax`

`1x1024`

`8192`

`double array`

caption caption = x = linspace(0,1,1024); y = exp(-128*((x-0.3).^2))-3*(abs(x-0.7).^0.4);

`caption`

is a string that contains the signal definition.Perform a Continuous Wavelet Transform.

Use the

`cwt`

command. Typec = cwt(cuspamax,1:2:64,'cgau4');

The arguments to

`cwt`

specify the signal to be analyzed, the scales of the analysis, and the wavelet to be used. The returned argument`c`

contains the coefficients at various scales. In this case,`c`

is a complex 32-by-1024 matrix, each row of which corresponds to a single scale.Plot the coefficients.

The

`cwt`

command accepts a fourth argument. This is a flag that, when present, causes`cwt`

to produce four plots related to the complex continuous wavelet transform coefficients:Real and imaginary parts

Modulus and angle

The

`cwt`

command can accept more arguments to define the different characteristics of the produced plots. For more information, see the`cwt`

reference page.Type

c = cwt(cuspamax,1:2:64,'cgau4','plot');

A plot appears:

Of course, coefficient plots generated from the command line can be manipulated using ordinary MATLAB graphics commands.

We now use the **Complex ****Continuous Wavelet 1-D** tool to analyze the
same cusp signal we examined using the command line interface in the
previous section.

Start the Complex Continuous Wavelet 1-D Tool.

From the MATLAB prompt, type

wavemenu

The

**Wavelet Toolbox Main Menu**appears.Click the

**Complex Continuous Wavelet 1-D**menu item.The continuous wavelet analysis tool for one-dimensional signal data appears.

Load a signal.

Choose the

**File > Load Signal**menu option.When the

**Load Signal**dialog box appears, select the MAT-file`cuspamax.mat`

, which should reside in the MATLAB folder`toolbox/wavelet/wavedemo`

. Click the**OK**button.The cusp signal is loaded into the

**Complex Continuous Wavelet 1-D**tool.The default value for the sampling period is equal to 1 (second).

Perform a Complex Continuous Wavelet Transform

To start our analysis, let's perform an analysis using the

`cgau4`

wavelet at scales 1 through 64 in steps of 2, just as we did using command-line functions in One-Dimensional Complex Continuous Wavelet Analysis.In the upper-right portion of the

**Complex Continuous Wavelet 1-D**tool, select the`cgau4`

wavelet and scales 1–64 in steps of 2.Click the

**Analyze**button.After a pause for computation, the tool displays the usual plots associated to the modulus of the coefficients on the left side, and the angle of the coefficients on the right side.

Each side has exactly the same representation that we found in Continuous Analysis Using the Graphical Interface.

Select the plots related to the modulus of the coefficients using the

**Modulus**option button in the**Selected Axes**frame.The figure now looks like the one in the real

**Continuous Wavelet 1-D**tool.

To know how to import and export information from the Complex Continuous Wavelet Graphical Interface, see the corresponding paragraph in Command Line Continuous Wavelet Analysis.

The only difference is that the variable `coefs`

is
a complex matrix (see Saving Wavelet Coefficients).

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