**Assignment 9** - Due Monday, 4/23/2018.

- Read sections 5.2 (Note: we covered this section, especially the
decomposition and reconstruction diagrams, in class on 4/16/18. The
only new thing is initialization.), 5.3.3 and 5.3.4.
- If you haven't formed a group for a project, do so by
Friday. Once you've done that, send me an email with a list of the
group members and a short description of the project.
- Problems.
- Chapter 5: 8(d,e,f), 11
- Do any two of the problems below.
- Write two programs in your favorite language to do the
following. Consider the $p_k$'s from the Example 5.25, p. 227
(Daubechies' wavelet; db2 in matlab). The first program inputs a
signal $a^j$ and outputs $a^{j-1}$ and $b^{j-1}$. It is the
decomposition step in a wavelet analysis. The second program inputs
$a^{j-1}$ and $b^{j-1}$ and outputs $a^j$. This is the
reconstruction step. In matlab, both programs involve the conv
(convolution) function, which will be used to filter inputs. In
addition, the first program requires a down-sampling part; the
second, up sampling.
- Let $f(t)=\begin{cases} t, & t \le \frac{3}{17}\\ 1.02t
+\frac{6.06}{17}, & \frac{3}{17} < t \end{cases}$. Sample $f$ at
$k 2^{-10}$, $k=0, \ldots, 1024 $. (The time interval is
$2^{-10}$, so $a^{10}_k$ corresponds to the time $k2^{-10}$.)
Either use matlab's wavemenu or the decomposition program from the
previous problem, applied to $a^{10}_k=f(k2^{-10})$ to obtain
$b^{-9}$. (The time interval is $2^{-9}$, $b^9_k$ corresponds to
the time $k2^{-9}= 2k2^{-10}$.) Keeping in mind the times
involved, plot both $a^{10}$ and $b^9$ versus $t$, $0\le t\le
1$. Can you detect the change in slope from the wavelet
coefficients?
- Chapter 5: 17
- Chapter 6: 2

- Write two programs in your favorite language to do the
following. Consider the $p_k$'s from the Example 5.25, p. 227
(Daubechies' wavelet; db2 in matlab). The first program inputs a
signal $a^j$ and outputs $a^{j-1}$ and $b^{j-1}$. It is the
decomposition step in a wavelet analysis. The second program inputs
$a^{j-1}$ and $b^{j-1}$ and outputs $a^j$. This is the
reconstruction step. In matlab, both programs involve the conv
(convolution) function, which will be used to filter inputs. In
addition, the first program requires a down-sampling part; the
second, up sampling.

- Chapter 5: 8(d,e,f), 11

Updated 4/17/2018