## Math 414 — Wavelet Toolbox Example

Here is an example of how to use the wavelet toolbox. Suppose that you
want to analyze a data file with a cat meowing, cat.wav; the ".wav"
extension is one of the standard formats for sound. Bring up
Matlab. Load the file using the command:
[ycat,srate] = audioread('cat.wav');

The row vector ycat contains the digitized sound samples
in double precision arithmetic. The variable srate is the
sampling rate in hertz - i.e, the number of samples per second. For
cat.wav, the number of samples in ycat is 10,319. The
rate is 11,025, or 11.025 kHz.

To do a wavelet analysis of ycat, first bring up the wavelet menu
with the command

wavemenu

This will bring up a window with various options for dding a wavelet
analysis. Since sound files are 1-D, go to the panel labeled
"One-Dimensional," then click on Wavelet 1-D. This will open a new
window. Click on file, and then on "import from Workspace." This
brings up a list variables in the workspace. Click
on ```
ycat. This loads ycat. The data loaded in
is displayed as a plot. You are now ready to do a wavelet analysis on
the data.
```

```
On the top of the right panel you will see written Wavelet and next to
that a drop down menu, with haar at the top. From the wavelets listed,
choose db, for Daubechies wavelet. Once you've done that, another drop
down menu appears. The number there refer to the wavelet type: db1 is
actually the Haar wavelet; db2 is the Daubechies wavelet that has N =
2 vanishing wavelet moments; db3 has N = 3 vanishing wavelet
moments. The number of p
```_{k}'s is 2N. Thus, for N =2, there
are four, p0, p1 ,p2, p3, whose values are given in the text.

```
Next, choose the decomposition level that you want to use. The
convention used in Matlab is opposite the one used in the text. The
finest level is 0 in Matlab. As the level increases, the levels become
coarser. For instance, if we have our starting level at j = 3, which
corresponds to 8 samples per second, the analysis would step down to j
= 2, then j = 1, j = 0, etc. The same analysis in Matlab would start
at level 0, then go to level 1, level 2, an finally stop at level
3. Once you've picked a level, click analyze. Try the various options
available to examine the data to display the wavelet decomposition.
```

```
Finally, the wavelet window has several options for dealing with the
data: compression and denoising being the standard options Of course,
there are a number of other things you can do, singularity detection,
for example. This is useful if you are looking for a change in
behavior of the signal.
```