📄 burg_s.m
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function [rc,var,ASAcontrol] = burg_s(f,b,max_order,last)
%BURG_S Burg type AR estimator for multiple segments
% [RC,VAR] = BURG_S(SIG_MTX,MAX_ORDER) estimates a single vector of AR-
% reflectioncoefficients RC up to order MAX_ORDER, using data from
% multiple segments simultaneously. The data segments must be of equal
% length and arranged columnwise in SIG_MTX. VAR is the estimated
% variance based on all elements of SIG_MTX.
%
% RC = BURG_S(F,B,ADD_ORDER) estimates ADD_ORDER additional
% reflectioncoefficients from matrices of forward and backward
% residuals F and B, that have been internally used in a previous Burg
% estimation procedure.
%
% Since forward and backward residual vectors are internally assigned
% to the ASAglob variables 'ASAglob_final_f' and 'ASAglob_final_b', an
% appropriate F and B can be retrieved after the program has finished
% execution. This is most easily done by typing:
% F = ASAglobretr('ASAglob_final_f');
% B = ASAglobretr('ASAglob_final_b');
%
% BURG_S is an ARMASA main function.
%
% See also: BURG, ASAGLOB, ASAGLOBRETR.
% References: S. de Waele and P. M. T. Broersen, The Burg Algorithm for
% Segments, IEEE Transactions on Signal Processing,
% vol. 48, no. 10, pp. 2876-2880, October 2000.
% W. Wunderink, The Introduction of a Computationally
% Efficient Burg Estimator Algorithm,
% Tech. Report SSC-March00-1, Delft University of
% Technology, Department of Applied Physics, Systems
% Signals and Control Group, the Netherlands, March 2000.
%Header
%==============================================================================
%Declaration of variables
%------------------------
%Declare and assign values to local variables
%according to the input argument pattern
switch nargin
case 1
if isa(f,'struct'), ASAcontrol=f;
else, error(ASAerr(39))
end
f=[]; b=[]; max_order=[];
case 2
if isa(b,'struct'), error(ASAerr(2,mfilename))
end
max_order=b; b=[]; ASAcontrol=[];
case 3
if isa(max_order,'struct'), ASAcontrol=max_order; max_order=b; b=[];
else, ASAcontrol=[];
end
case 4
if isa(last,'struct'), ASAcontrol=last;
else, error(ASAerr(39))
end
otherwise
error(ASAerr(1,mfilename))
end
state = 0;
if isequal(nargin,1) & ~isempty(ASAcontrol)
%ASAcontrol is the only input argument
ASAcontrol.error_chk = 0;
ASAcontrol.run = 0;
elseif (isequal(nargin,3) & isempty(ASAcontrol)) | ...
isequal(nargin,4) %f and b have been provided
%as input arguments (empty b not excluded)
state = 1;
end
%Declare ASAglob variables
ASAglob = {'ASAglob_final_f';'ASAglob_final_b'};
%Assign values to ASAglob variables by screening the
%caller workspace
for ASAcounter = 1:length(ASAglob)
ASAvar = ASAglob{ASAcounter};
eval(['global ' ASAvar]);
if evalin('caller',['exist(''' ASAvar ''',''var'')'])
eval([ASAvar '=evalin(''caller'',ASAvar);']);
else
eval([ASAvar '=[];']);
end
end
%ARMASA-function version information
%-----------------------------------
%This ARMASA-function is characterized by
%its current version,
ASAcontrol.is_version = [2000 12 30 20 0 0];
%and its compatability with versions down to,
ASAcontrol.comp_version = [2000 12 30 20 0 0];
%This function calls other functions of the ARMASA
%toolbox. The versions of these other functions must
%be greater than or equal to:
ASAcontrol.req_version.convolrev = [2000 12 6 12 17 20];
%Checks
%------
if ~any(strcmp(fieldnames(ASAcontrol),'error_chk')) | ASAcontrol.error_chk
%Perform standard error checks
%Input argument format checks
ASAcontrol.error_chk = 1;
if ~isnum(f)
error(ASAerr(11,'f'))
elseif isavector(f) & size(f,2)>1
f = f(:);
warning(ASAwarn(25,{'row';'f';'column'},ASAcontrol))
elseif ~(length(size(f))==2)
error(ASAerr(35,'f'))
end
if ~isavector(f)
warning(ASAwarn(36,ASAcontrol))
end
if ~isempty(b)
if ~isnum(b)
error(ASAerr(11,'b'))
elseif isavector(b) & size(b,2)>1
b = b(:);
warning(ASAwarn(25,{'row';'b';'column'},ASAcontrol))
elseif ~(length(size(b))==2)
error(ASAerr(35,'b'))
end
end
if ~isnum(max_order) | ~isintscalar(max_order) | ...
max_order<0
error(ASAerr(17,'max_order'))
end
%Input argument value checks
if ~isreal(f) | (~isempty(b) & ~isreal(b))
error(ASAerr(13))
end
if isempty(b)
if max_order>size(f,1)-1
error(ASAerr(21))
end
elseif ~isequal(size(f),size(b))
error(ASAerr(28,{'f','b'}))
elseif max_order>size(f,1)-2
error(ASAerr(29,'max_order'))
end
end
if ~any(strcmp(fieldnames(ASAcontrol),'version_chk')) | ASAcontrol.version_chk
%Perform version check
ASAcontrol.version_chk = 1;
%Make sure the requested version of this function
%complies with its actual version
ASAversionchk(ASAcontrol);
%Make sure the requested versions of the called
%functions comply with their actual versions
convolrev(ASAcontrol);
end
if ~any(strcmp(fieldnames(ASAcontrol),'run')) | ASAcontrol.run
%Run the computational kernel
ASAcontrol.run = 1;
ASAcontrol.version_chk = 0;
ASAcontrol.error_chk = 0;
%Main
%==========================================================================
[N,n] = size(f);
P = max_order;
if P>0
%The protocol is tuned using Matlab R12,
%but also works fine on R11.
if ~isempty(b)
P = P+1;
protocol = [0 3 0;0 0 0;0 0 0;0 P 0];
else
if N<128
protocol = [0 3 0;0 0 0;0 0 0;0 P 0];
elseif N<12000 %C_7 (& C_13)
if P<(0.1+6.7e-006*N)*N %C_14 & S
protocol = [0 1 0;0 0 0;0 0 0;0 P 0];
else
protocol = [0 3 0;0 0 0;0 0 0;0 P 0];
end
else
if P<0.18*N %S
protocol = [0 1 0;0 0 0;0 0 0;0 P 0];
else
protocol = [0 1 3 0;0 0 0 0;0 1 0 0;0 round(0.03*N) P 0]; %C_5
end
end
end
else
protocol = zeros(4,2);
end
p = 0;
p_max = 0;
i2 = 2;
while protocol(4,i2)~=0;
p = protocol(4,i2)-protocol(4,i2-1);
if p>p_max
p_max = p;
end
i2 = i2+1;
end
i9 = 1;
i10 = 2;
if n>N
i9 = 2;
i10 = 1;
end
v = zeros(N+p_max,n,2);
a = zeros(N+p_max,n,2);
if isempty(b)
v(1:N,:,2) = f;
a(1+p_max:N+p_max,:,2) = f;
if protocol(1,2)==3 | protocol(1,2)==0
var = sum(sum(f(1:N,:).^2,i9),i10)/(n*N);
den = 2*var*n*N;
end
else
v(1:N,:,2) = f;
a(1+p_max:N+p_max,:,2) = b;
den = sum(sum(f(1:N,:).^2+b(1:N,:).^2,i9),i10);
var = [];
end
r1 = p_max+1;
v1 = [1 1];
v2 = [N N];
v3 = [N N];
a1 = [r1 r1];
a2 = [r1 r1];
a3 = [r1+N-1 r1+N-1];
rc = zeros(1,P+1);
i1 = 0;
i2 = 2;
i4 = 0;
c = 0;
while protocol(4,i2)~=0
i1 = i1+1;
p = protocol(4,i2);
if protocol(1,i2)==3 %SP
r2 = a2(1)+1;
r3 = v2(1)-1;
r4 = a2(2)+1;
r5 = v2(2)-1;
i5 = i1;
for i1 = i1:p
i5 = i5+1;
if c, c0 = 2; c1 = 1;
else c0 = 1; c1 = 2;
end
v1(c0) = v1(c1)+1;
a3(c0) = a3(c1)-1;
v(v1(c0):v2(c0),:,c0) = v(v1(c0):v2(c1),:,c1)+...
rc(i1)*a(r4:a3(c1),:,c1);
a(a2(c0):a3(c0),:,c0) = a(a2(c1):a3(c0),:,c1)+...
rc(i1)*v(v1(c1):r5,:,c1);
den = (1-rc(i1)^2)*den-...
sum((v(v1(c1),:,c1)+rc(i1)*a(a2(c1),:,c1)).^2)-...
sum((a(a3(c1),:,c1)+rc(i1)*v(v2(c1),:,c1)).^2);
rc(i5) = -2*sum(sum(v(v1(c0):v2(c0),:,c0).*...
a(a2(c0):a3(c0),:,c0),i9),i10)/den;
c = ~c;
end
v(v1(c1),:,c0) = v(v1(c1),:,c1)+rc(i1)*a(a2(c1),:,c1);
a(a3(c1),:,c0) = a(a3(c1),:,c1)+rc(i1)*v(v2(c1),:,c1);
elseif protocol(1,i2)==1 %ACC
i13 = 2*p;
i14 = p+1;
i15 = 0;
i16 = 0;
i17 = 0;
jj = zeros(2,i13);
jjm_h = zeros(2,i14);
jj_h = zeros(2,i14);
jj(2,1) = 1;
jjm_h(2,1) = 1;
jj_h(2,2) = 1;
for i4 = 1:n
acov_x(:,i4) = convolrev(f(:,i4),p,ASAcontrol);
end
i1 = i1+1;
var = sum(acov_x(1,:));
den = (2*var-sum(v(v1(2),:,2).^2)-sum(a(a3(2),:,2).^2));
rc(i1) = -2*sum(acov_x(2,:))/den;
var = var/(n*N);
v1(2) = v1(2)+1;
a3(2) = a3(2)-1;
t = 0;
r5 = v1(2)+p-2;
r6 = a3(2)-p+2;
if protocol(3,i2)==1
r11 = r5+1;
r12 = r6-1;
i33 = 0;
else
r11 = v2(2)-p+2;
r12 = a2(2)+p-2;
i33 = 1;
end
r7 = v2(2)+1;
r8 = a2(2)-1;
r9 = v1(2);
r10 = a3(2);
r13 = r5-r9;
r14 = r10-r6;
r15 = r11-r9;
r16 = r10-r12;
for i1 = i1:p
i13 = i1+1;
i14 = i1-1;
i15 = 2*i1-1;
i16 = 2*i1-2;
i17 = 2*i1-3;
rc_h1 = rc(i1)^2;
rc_h2 = 2*rc(i1);
if c, c0 = 2; c1 = 1;
else c0 = 1; c1 = 2;
end
jj(c0,1:2) = jj(c1,1:2);
jj(c0,3:i15) = jj(c1,3:i15)+rc_h1*jj(c1,i17:-1:1);
jj(c0,i1:i16) = jj(c0,i1:i16)+rc_h2*jjm_h(c1,1:i14);
jj(c0,2:i14) = jj(c0,2:i14)+rc_h2*jjm_h(c1,i14:-1:2);
jjm_h(c0,1:i1) = rc(i1)*jj_h(c1,1:i1);
jjm_h(c0,1:i14) = jjm_h(c0,1:i14)+(1+rc(i1)^2)*jjm_h(c1,1:i14);
jj_h(c0,1:i13) = jj(c0,i13:-1:1);
jj_h(c0,1:i14) = jj_h(c0,1:i14)+jj(c0,i13:i15);
va_t(1,:) = jj(c0,1:i1)*acov_x(i13:-1:2,:);
va_t(2,:) = jj(c0,i13:i15)*acov_x(1:i14,:);
v1(c0) = v1(c1)+1; v3(c0) = v3(c1)+1;
a1(c0) = a1(c1)-1; a3(c0) = a3(c1)-1;
t = t+i33;
v(r9:r5,:,c0) = v(r9:r5,:,c1)+...
rc(i1)*a(a1(c1):a1(c1)+r13,:,c1);
v(r11+t:v3(c1),:,c0) = v(r11+t:v3(c1),:,c1)+...
rc(i1)*a(a1(c1)+r15+t:r10,:,c1);
v(v3(c0),:,c0) = rc(i1)*f(N,:);
a(r6:r10,:,c0) = a(r6:r10,:,c1)+...
rc(i1)*v(v3(c1)-r14:v3(c1),:,c1);
a(a1(c1):r12-t,:,c0) = a(a1(c1):r12-t,:,c1)+...
rc(i1)*v(r9:v3(c1)-r16-t,:,c1);
a(a1(c0),:,c0) = rc(i1)*f(1,:);
omega_va(c0) = sum(sum(v(r9:v1(c1),:,c0).*a(a1(c0):r8,:,c0)+...
v(r7:v3(c0),:,c0).*a(a3(c1):r10,:,c0),1));
den = den*(1-rc_h1)-sum(v(v1(c1),:,c0).^2)-sum(a(a3(c1),:,c0).^2);
rc(i13) = -2*(sum(sum(va_t,2),1)-omega_va(c0))/den;
c=~c;
end
i1 = p;
end
i2 = i2+1;
end
if state %f and b have been provided as input
%arguments (empty b not excluded)
if isempty(b)
rc = rc(2:end);
else
rc = rc(3:end);
end
else
rc(1) = 1;
end
i2 = i2-1;
ASAglob_final_f = [];
ASAglob_final_b = [];
if protocol(3,i2)==1 | protocol(1,i2)==3
ASAglob_final_f = v(v1(c1):v2(c0),:,c0);
ASAglob_final_b = a(a2(c0):a3(c1),:,c0);
elseif isequal(P,0)
ASAglob_final_f = f;
end
%Footer
%=====================================================
else %Skip the computational kernel
%Return ASAcontrol as the first output argument
if nargout>1
warning(ASAwarn(9,mfilename,ASAcontrol))
end
rc = ASAcontrol;
ASAcontrol = [];
end
%Program history
%======================================================================
%
% Version Programmer(s) E-mail address
% ------- ------------- --------------
% former version S. de Waele waele@tn.tudelft.nl
% [2000 12 30 20 0 0] W. Wunderink wwunderink01@freeler.nl
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