bpfig26.m

％ Atomizer Main Directory, Version .802 里面信号含有分解去噪合成过程的代码 ％---------------------------------------

% bpfig26: BP Figure 2.6 -- Analyzing WernerSorrows
%----------------------------------------------------------------------
%
%    (1) BOB by C-W entropy can be improved by BOB by l^1 entropy.
%    (2) BOB by l^1 entropy can be improved by BP.
%
% Signal:        WernerSorrows
% Signal Length: 1024
% Dictionary:    Cosine Packets with D = log2(n)-4
% Observations:
%    (a) Signal: WernerSorrows, a signal made up of a sinusoid and
%	 two chirps.
%    (b) Phase plane from BOB by C-W entropy(like l^2). BOB chooses
%	 Fourier basis, and totally fails to find the chirp structures.
%    (c) Phase plane from BOB by l^1 entropy. We can basically observe
%	 the three structures in the signal.
%    (d) Phase plane from BP. Compared with (c), BP clearly 
%        reveals the sinusoid and the two chirps.
%
% Use:
%    bpfig26                   uses the current solver.
%    ATOMIZER_ENGINE = 1998;   selects original solver.
%    ATOMIZER_ENGINE = 2001;   selects later    solver.
%    Default is most recent solver.
%----------------------------------------------------------------------

%----------------------------------------------------------------------
%        1998: (S. Chen) Original script for BP paper.
% 09 Apr 2001: (M. Saunders) Choice of solvers implemented.
%----------------------------------------------------------------------

help bpfig26
bpengine;

n    = 1024;
D    = log2(n); 
t    = (1:n)' ./ n;
bell = 'Sine';
x    = InputSignal('WernerSorrows',n);

%--------------------------------------
% BOB with Coifman-Wickerhauser Entropy
%--------------------------------------
cBOB1 = BOB(x, 'CP', D-4, bell, 0, 'Entropy');

%-------------------------------------
% BOB with l^1 Entropy
%-------------------------------------
time  = cputime;
cBOB2 = BOB(x, 'CP', D-4, bell, 0, 'l^p', 1);
time2 = cputime - time;

%-------------------------------------
% BP
%-------------------------------------
time  = cputime;
switch ATOMIZER_ENGINE
  case 1998
    cBP = BP_Interior ( x, 'CP', D-4, bell, 0 );
  case 2001
    cBP = BP_Interior2( x, 'CP', D-4, bell, 0 );
end
time4 = cputime - time;

fprintf('\n')
fprintf('CPU Running Time of BOB = %8.4e\n', time2);
fprintf('CPU Running Time of  BP = %8.4e\n', time4);

%--------------------
% Plots
%--------------------
fprintf('\nConstructing figure(%1g) ...\n', FIGURE)
figure(FIGURE);   clf reset;

TFNORM = 64.5218;
subplot(2,2,1);   plot(t,x);
                  title('(a) Signal: Werner Sorrows')
subplot(2,2,2);   PhasePlane(cBOB1, 'CP', n, 0, 256, TFNORM);
                  title('(b) Phase Plane: BOB by C-W Entropy')
subplot(2,2,3);   PhasePlane(cBOB2, 'CP', n, 0, 256, TFNORM);
                  title('(c) Phase Plane: BOB by l^1 Entropy')
subplot(2,2,4);   PhasePlane(cBP  , 'CP', n, 0, 256, TFNORM);
                  title('(d) Phase Plane: BP')