# PhD Course

## Time-Frequency Analysis

### Examples

During the November session I showed a number of examples using the Uvi_Wave toolbox. Links to the m-files with the examples are below, with brief descriptions.
• The time-frequency plane plotting function is in tfp4.m. It is needed for the following examples.
• The example with superposition of three sines is in ajfreqloc.m.
• The example with three time events is in ajtimeloc.m.
• The example combining the two types of signals above is in ajtimefreqloc.m
• The example using the best basis algorithm with Shannon entropy and lp-norm as the cost functions is in ajpacketex.m. The example also shows the result of the specgram function from the signal processing toolbox. Comment out, if you do not have access to this toolbox.

### Exercises

As part of the course you are asked to do some exercises. The first two exercises are fairly well defined, the third one is open-ended. The fourth one requires some care in interpretation, and shows how one can manipulate the plots.
1. In each of the four examples above experiment with the various parameters. Change the length of the filter. Note that for the Daubechies filters the length must be even. Try to change to other filters. Possibilities include symlets, see
```help symlets
```
and the CDF-family described in the lectures, see
```help wspline
```
Try changing the level of the best level basis used for the first plot in the first three examples (see comments in the m-files). In the wavelet packet with cost function lp-norm try changing the value of the p-parameter. In the original m-file it is 1.5.
2. Replace the signal in the examples with another synthetic signal.
3. Use the experience you have gained in the two exercises above to analyse some real-life signals.
4. The file tfp4.m uses a transformation of the wavelet packet coefficients, before the plot is made. They are in line 58
```Y2 = log(abs(Y2)+1);
```
and in line 72,
```(col^2)
```
Try replacing the power 2 by 1. Try other transformations. Compare the plots in the different cases, when you repeat the above computatins in the examples with this modified plotter.