function P = best_chirplet(x, level, M, verbose, c, d, t, f)% best_chirplet -- find the chirplet that best fits the signal% %  Usage%    P = best_chirplet(x, level, M, verbose, c, d, t, f)%%  Inputs%    x         signal%    level     level of difficulty, 0 (easiest) -> 3 (hardest) (optional,%              default is 2)%    M         resolution parameter (optional, default is 64)%    verbose   verbose flag (optional, default is 0)%    c,d,t,f   possible intializations; level 0 uses c, d, t, and f;%              level 1 uses c and d; (optional, defaults are 0, 50, N/2 and%              0, respectively)%%  Outputs%    P    vector of chirplet parameters (see chirplets.m)%% level 0: quasi-Newton (QN)% level 1: est_tf -> est_c -> est_d -> QN% level 2: est_cd_global -> est_tf -> est_c -> est_d -> QN% level 3: est_cd_global -> (est_tf -> est_c -> est_d) x 3 -> QN% Copyright (C) -- see DiscreteTFDs/Copyrighterror(nargchk(1,8,nargin));x = x(:);N = length(x);% this works better numericallye = norm(x);x = x/e;if (nargin<2) level = 2; endif (nargin<3) M = 64; endif (nargin<4) verbose = 0; endif (nargin<5) c = 0; endif (nargin<6) d = 50; endif (nargin<7) t = N/2; endif (nargin<8) f = 0; endif (level~=0 & level~=1 & level~=2 & level~=3)  error('choose a valid level')end% estimate chirp-rate and duration globallyr = 5; % robustness parameterif (level == 2 | level == 3)  [c, d] = est_cd_global(x, M, r);  if (verbose) fprintf(1,'est_cd_global -> c = %7.4f, d = %6.2f\n', c, d), endendif (level == 1 | level == 2)  [t f] = est_tf(x, c, d, M);  f = mod(f, 2*pi);  if (verbose) fprintf(1,'est_tf -> t = %7.2f, f = %4.2f\n', t, f), end  c = est_c(x, t, f, M);  if (verbose) fprintf(1,'est_c -> c = %7.4f\n', c), end  d = est_d(x, t, f, c, M);  if (verbose) fprintf(1,'est_d -> d = %6.2f\n', d), endelseif (level == 3)  for i=1:3,    [t f] = est_tf(x, c, d, M);    f = mod(f, 2*pi);    if (verbose) fprintf(1,'est_tf -> t = %7.2f, f = %4.2f\n', t, f), end    c = est_c(x, t, f, M);    if (verbose) fprintf(1,'est_c -> c = %7.4f\n', c), end    d = est_d(x, t, f, c, M);    if (verbose) fprintf(1,'est_d -> d = %6.2f\n', d), end  endend% do a quasi-Newton maximization on the windowed signal% a longer window is useful here.Z = 4;rt = round(t);if ( (rt-Z*M < 1) & (rt+Z*M > N) )  xx = [zeros(Z*M-rt+1,1) ; x ; zeros(Z*M-N+rt,1)];elseif (rt-Z*M < 1)  xx = [zeros(Z*M-rt+1,1) ; x(1:rt+Z*M)];elseif (rt+Z*M > N)  xx = [x(rt-Z*M:N) ; zeros(Z*M-N+rt,1)];else  xx = x(rt-Z*M:rt+Z*M);endopt = foptions;P = constr('f_chirp',[Z*M+1+(t-rt) f c d],opt,[1 0 -inf .25],[2*Z*M+1 2*pi inf N/2],'g_chirp',xx);P(1) = rt + P(1) - (Z*M+1);P(2) = mod(P(2),2*pi);if (verbose) fprintf(1,'constr -> t = %7.2f, f = %4.2f, c = %7.4f, d = %6.2f\n', P), endy = chirplets(N, [1 P]);A = y'*x;A = A*e;P = [A P];