18.327 and 1.130

Joint course on


18.327 - Wavelets and Filter Banks

Gilbert Strang

1.130 - Wavelets and Multiscale Methods in
Engineering Computation and Information Processing

Kevin Amaratunga


18.327/1.130 has been published through MIT OpenCourseWare: OCW version of 18.327/1.130


Gilbert Strang e-mail: gs@math.mit.edu Office: Room 2-240. 
Kevin Amaratunga e-mail: kevina@mit.edu Office: Room 1-274. 

Schedule for Spring 2004:    Monday and Wednesday 1:30-3:00 in Room 1-390.

Text:           WAVELETS AND FILTER BANKS by Strang and Nguyen, Wellesley-Cambridge Press, 2nd Ed. (1997.)

Syllabus:      Please see the class schedule. Also, see the course announcement for general course overview.








Matlab routines

Matlab examples

Java Applets (by Pavel Grinfeld)

Matlab Minicourses

2/9 @12 noon and 7pm, and 2/10 @12 noon and 7pm, Room 3-343.

Matlab Wavelet Toolbox

The Matlab wavelet toolbox (v 2.2) is available as part of the Matlab installation on Athena. Launch Matlab (v 6.5.1 is the default) and type "help wavelet" at the Matlab prompt for a list of available wavelet toolbox commands. For a demo of the wavelet toolbox type "wavedemo".

To launch the graphical user interface for the Matlab wavelet toolbox, type "wavemenu" at the Matlab prompt. For starters, try selecting "Wavelet 1-D", then go to "File | Load Signal". To locate the sample signals on Athena, type the following path into the "Filter" field and hit the return key.


You will then be able to choose a signal from the list of files. A good one to start with is noisdopp.mat. Once the signal has loaded, choose a wavelet and the number of decomposition levels. The default wavelet filter is "haar". To use the Daubechies 4-tap filter, for example, you would choose "db2". The 2 means that the frequency response has 2 zeros at pi. Similarly, to use the linear phase 9/7 filters, you would choose "bior4.4". In this case, 4.4 means that the synthesis lowpass filter has 4 zeros at pi and the analysis lowpass filter has 4 zeros at pi (in that order.) Next, click "Analyze" to perform the wavelet analysis. You will then see graphs of the original signal (s) and the various subbands of the signal (an,dn,...,d1) where n is the number of levels. Note that the subband signals are of full length in this display. In other words, what is being displayed is not the actual coefficients produced in the output of the analysis bank, but the reconstructed version of each channel that is seen in the synthesis filter bank immediately prior to recombining the channels. Note that you can look at the statistics of the signal and even compress or denoise it.

The "Wavelet 2-D" menu item should be straightforward to use once you have seen the 1-D version. A good image to start with is woman.mat, which is the famous Barbara image.

Also interesting to beginners is the "Wavelet Display" menu item. This allows you to view the scaling function(s) and wavelet(s) and their associated filters.


User's Guide for the Matlab Wavelet Toolbox.


Please send suggestions to 18.327/1.130 webmaster.