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Order terminal nodes of binary wavelet packet tree
[Tn_Pal,Tn_Seq]
= otnodes(WPT)
[Tn_Pal,Tn_Seq,I,J]
= otnodes(WPT)
[DP_Pal,DP_Seq]
= otnodes(WPT,'dp')
[Tn_Pal,Tn_Seq] = otnodes(WPT) returns the terminal nodes of the binary wavelet packet tree, WPT, in Paley (natural) ordering, Tn_Pal, and sequency (frequency) ordering, Tn_Seq. Tn_Pal and Tn_Seq are N-by-1 column vectors where N is the number of terminal nodes.
[Tn_Pal,Tn_Seq,I,J] = otnodes(WPT) returns the permutations of the terminal node indices such that Tn_Seq = Tn_Pal(I) and Tn_Pal = Tn_Seq(J).
[DP_Pal,DP_Seq] = otnodes(WPT,'dp') returns the Paley and frequency-ordered terminal nodes in node depth-position format. DP_Pal and DP_Seq are N-by-2 matrices. The first column contains the depth index, and the second column contains the position index.
WPT |
Binary wavelet packet tree. You can use treeord to determine the order of your wavelet packet tree. |
dp |
String variable indicating that the Paley-ordered or sequency-ordered nodes are returned in depth-position format. |
Tn_Pal |
Terminal nodes in Paley (natural) ordering |
Tn_Seq |
Terminal nodes in sequency ordering |
DP_Pal |
Paley-ordered terminal nodes in depth-position format. This output argument only applies when you use the 'dp' input argument. |
DP_Seq |
Sequency-ordered terminal nodes in depth-position format. This output argument only applies when you use the 'dp' input argument. |
Order terminal nodes with Paley and frequency ordering:
x = randn(8,1); wpt = wpdec(x,2,'haar'); [Tn_Pal,Tn_Seq] = otnodes(wpt); % Tn_Pal is [3 4 5 6] % Tn_Seq is [3 4 6 5]
Return permutations for Paley and frequency ordering:
load noisdopp; wpt = wpdec(noisdopp,6,'sym4'); [Tn_Pal,Tn_Seq,I,J] = otnodes(wpt); isequal(Tn_Seq(J),Tn_Pal) isequal(Tn_Seq,Tn_Pal(I))
Order terminal nodes by depth and position:
x = randn(8,1); wpt = wpdec(x,2,'haar'); [DP_Pal,DP_Seq] = otnodes(wpt,'dp');
Order terminal nodes from a modified wavelet packet tree:
t = wptree(2,2,rand(1,512),'haar'); t = wpsplt(t,4); t = wpsplt(t,5); t = wpsplt(t,10); plot(t); [tn_Pal,tn_Seq,I,J] = otnodes(t);
Wickerhauser, M.V. Lectures on Wavelet Packet Algorithms, Technical Report, Washington University, Department of Mathematics, 1992.