# Faculty of Engineering and Science

The International Doctoral School of Technology and Science

#
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.
- 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.
- Replace the signal in the examples with another synthetic signal.
- Use the experience you have gained in the two exercises above
to analyse some real-life signals.
- 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.

This page is maintained by Arne
Jensen.

Updated November 18, 2003, Arne Jensen.