Examples Using Wavelet Packet Tree Objects

You can use command line functions, the Wavelet Analyzer app, or you can mix both of them to work with wavelet packet trees (WPTREE objects). The most useful commands are

plot, drawtree, and readtree, which let you plot and get a wavelet packet tree
wpjoin and wpsplt, which let you change a wavelet packet tree structure
get, read, and write, which let you read and write coefficients or information in a wavelet packet tree

We can see some of these features in the following examples.

plot and wpviewcf

load noisbump
x = noisbump;
t = wpdec(x,3,'db2');
fig = plot(t);

Click on node 7.

Change Node Action from Visualize to Split-Merge and merge the second node.

% From the command line, you can get the new tree.
newt = plot(t,'read',fig);

% The first argument of the plot function in the last command
% is dummy. Then the general syntax is:
%    newt = plot(DUMMY,'read',fig);
% where DUMMY is any object parented by an NTREE object.
% DUMMY can be any object constructor name, which returns
% an object parented by an NTREE object. For example:
%    newt = plot(ntree,'read',fig);
%    newt = plot(dtree,'read',fig);
%    newt = plot(wptree,'read',fig);

% From the command line you can modify the new tree,
% then plot it.
newt = wpjoin(newt,3);
fig2 = plot(newt);

% Change Node Label from Depth_position to Index and
% click the node (3). You get the following figure.

% Using plot(newt,fig), the plot is done in the figure fig,
% which already contains a tree object.

% You can see the colored wavelet packets coefficients using
% from the command line, the wpviewcf function (type help
% wpviewcf for more information).
wpviewcf(newt,1)

% You get the following plot, which contains the terminal nodes
% colored coefficients.

drawtree and readtree

load noisbump
x = noisbump;
t = wpdec(x,3,'db2');
fig = drawtree(t);

% The last command creates a GUI. 
% The same GUI can be obtained using waveletAnalyzer and:
% - clicking the Wavelet Packet 1-D button,
% - loading the signal noisbump,
% - choosing the level and the wavelet
% - clicking the decomposition button. 
% You get the following figure.

% From the app, you can modify the tree. 
% For example, change Node label from Depth_Position to Index, 
% change Node Action from Visualize to Split_Merge and 
% merge the node 2. 
% You get the following figure.

% From the command line, you can get the new tree.
newt = readtree(fig);

% From the command line you can modify the new tree;
% then plot it in the same figure.
newt = wpjoin(newt,3);
drawtree(newt,fig);

You can mix previous commands. The GUI associated with the plot command is simpler and quicker, but more actions and information are available using portions of the Wavelet Analyzer app related to wavelet packets.

The methods associated with WPTREE objects let you do more complicated actions.

Namely, using read and write methods, you can change terminal node coefficients.

Let's illustrate this point with the following “funny” example.

Change Terminal Node Coefficients

load gatlin2
t = wpdec2(X,1,'haar');
plot(t);
% Change Node Label from Depth_position to Index and
% click the node (0). You get the following figure.

% Now modify the coefficients of the four terminal nodes.
newt = t;
NBcols = 40;

for node = 1:4
  cfs = read(t,'data',node);
  tmp = cfs(1:end,1:NBcols);
  cfs(1:end,1:NBcols) = cfs(1:end,end-NBcols+1:end);
  cfs(1:end,end-NBcols+1:end) = tmp;
  newt = write(newt,'data',node,cfs);
end
plot(newt)

% Change Node Label from Depth_position to Index and
% click on the node (0). You get the following figure.

You can use this method for a more useful purpose. Let's see a denoising example.

Thresholding Wavelet Packets

load noisbloc
x = noisbloc;
t = wpdec(x,3,'sym4');
plot(t);
% Change Node Label from Depth_position to Index and
% click the node (0). You get the following plot.

% Global thresholding.
t1 = t;
sorh = 'h';
thr = wthrmngr('wp1ddenoGBL','penalhi',t);
cfs = read(t,'data');
cfs = wthresh(cfs,sorh,thr);
t1  = write(t1,'data',cfs);
plot(t1)

% Change Node Label from Depth_position to Index and
% click the node (0). You get the following plot.

% Node by node thresholding. 
t2 = t;
sorh = 's';
thr(1) = wthrmngr('wp1ddenoGBL','penalhi',t);
thr(2) = wthrmngr('wp1ddenoGBL','sqtwologswn',t);
tn  = leaves(t);
for k=1:length(tn)
  node = tn(k);
  cfs = read(t,'data',node);
  numthr = rem(node,2)+1;
  cfs = wthresh(cfs,sorh,thr(numthr));
  t2 = write(t2,'data',node,cfs);
end
plot(t2)

% Change Node Label from Depth_position to Index and
% click the node (0). You get the following plot.

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