# Documentation

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## DFT-Based Continuous Wavelet Analysis Using the Wavelet Analyzer App

You can use the Continuous Wavelet 1-D (Using FFT) tool to perform continuous wavelet analysis.

1. At the MATLAB® command prompt, enter

`waveletAnalyzer`

2. Click the Continuous Wavelet 1-D (Using FFT) menu item.

3. At the MATLAB command prompt, type

`load noisdopp;`
In the Continuous Wavelet 1-D (Using FFT) tool, select File > Import from Workspace. When the Import from Workspace dialog box appears, select the `noisdopp` variable. Click OK to import the data.

4. Using the menu default parameters, click Analyze.

5. Reconstruct the signal based on all the default dyadic scales. Click Scales Selection.

Select all scales by clicking All. Click Synthesize.

In the top left, the synthesized signal plot is superimposed on the original signal. The relative maximum and L2 errors are displayed under the plot.

The single integral CWT inversion does not produce perfect reconstruction, but the relative errors using the default logarithmically–spaced scales are small.

6. Obtain a signal approximation from selected scales.

Click None in the Selection of Scales panel to undo the scale selection. Then, select only scale indices greater than 10 and reconstruct an approximation to the original signal. Hold the `Ctrl` key while selecting scale indices 11–21. The scale indices correspond to the following physical scales.

```dt = 1; s0 = 2*dt; ds = 0.4875; nb = 21; physical_scales = s0*pow.^((0:nb-1)*ds);```
7. Click Synthesize.

The reconstructed signal from scale indices 11–21 is a lowpass approximation to the noisy Doppler signal.

8. Analyze using linear scales. In the Scales drop-down menu in the upper right, select `Linear default` and click Analyze.

### Note

The other options under Scales include ```Dyadic default``` and `Manual`.

If you select `Manual`, a Define Scales button appears. Click Define Scales to set the parameters for your scale vector.

### Manual Selection of CWT Coefficients

Select coefficients manually by graphically selecting the CWT coefficients. Reconstruct the signal from the selected coefficients. Click Manual Selection of Coefficients. The Select the Coefficients Manually panel appears with a single box containing all the CWT coefficient moduli.

You can change the CWT coefficient view to `Angle`, `Real`, or `Imaginary`.

To select a subset of coefficients, draw a box by left-clicking and dragging the mouse. When you release the mouse button, a semi-transparent box with a green border is superimposed on the plot.

You can place multiple boxes on the same plot. To synthesize a signal based on the selected coefficients, click Synthesize.

To select, unselect, or delete a box, right-click in the box. A context menu appears that allows you to select, unselect, or delete the box. After you select the coefficients within the box, the border of the box displays in green. When the coefficients within the box are not selected, the border of the box displays in red.

imYou can move a box by clicking the left mouse button inside the box while simultaneously pressing the `Shift` key. The border of the box changes to yellow, and you can drag the box to the desired location. You must keep the `Shift` key pressed while you are moving the box.

Quit the manual selection mode by clicking the Close button.

In the Show synthesized signals from panel on the right, you can turn the plot of your synthesized signal on and off by checking and unchecking Manual selection.

Using the File > Save > Synthesized signal menu, you can save the available synthesized signals.

Using the File > Save > Decomposition menu, you can save the wavelet analysis as a `MAT` file.

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