R. Robinson 11/99, 4/01

This lab is an extension of lab 9. Do just one of the two.
 
There are two parts:

1. Solve for the wavelet coefficients in the DAUB4 and DAUB 6 cases (in the case of DAUB4 you will be confirming what I stated in class)...and

2. Implement the discrete wavelet transform assuming the number of data points is a power of 2.  There is a fast wavelet transform, but we will do it by matrix multiplication.

You may use Maple or Matlab. I recommend using Maple at least for part 1 and seeing if you can get it to give an exact solution. On the other hand, implementing the transfrom will probably be easier in Matlab.

If you use Maple you should begin by typing

> with (linalg);

(to load the linear algebra package) and look at "help" on commands "matrix", "augment", "stackmatrix" etc.

Matrix multiplication in Maple is denoted by "&*".

You sometimes need to evaluate a matrix with "evalm" to see its entries.

3. In the case of a fairly large number of data points, draw some graphs of wavelet bases. Do this by plugging in the vectors [0,0,0,...,0,1,0,...0] to the inverse transform (i.e., the transpose). If the graph "wraps around" move the location of the 1. Compare DAUB4 (fractal looking!) and DAUB6.