1. Prove (4.2), page 104 of the text.
(phi_{jk} should be phi_{jl})


2.  In example 4.2.1 (p. 106), what
is

(a)  \psi(1/2), \psi(1), \psi(3/2).$

(b) \phi(1/4)

3. The Wavelab commands 
  filt=MakeONFilter('Daubechies',4)
  a=FWT_PO([1 0 -3 2 1 0 1 2], 1, filt)

give:
a =

  Columns 1 through 8 

   -0.0490  2.0490  1.1830  0.8170 -0.2588  3.6049  -0.7765  0.2588

What are the matrices H_1, G_1, H_2, G_2 in the example 4.3.2?

4. Extra Credit

(S-Plus Assignment)
For the first 256 measurements of geyser$waiting in the geyser
data set find the best Pollen's 4 tap wavelet.
(best in the sense that it minimizes the entropy of the data-energy
in the wavelet domain). 

Plot ``the best wavelet.'' Use Daubechies-Lagarias algorithm
(http://www.isds.duke.edu/~brani/Wiley/software.html).