function??[y??A]=?sparseBSS1（XLlangdaGhdelta）
%----------------------------------------------------------------
%??????????????????2009-04-15?YangZhicong
%?X:?observed?signaleach?row?correspond?to?a?sensor?observations
%?L:?the?length??of?FFT?（or?the?length?of?Hanning?window）
%?langda:?adjust?the?desired?angular?width
%?G:?%?discretize?the?potential?field?by?taking?a?sample?of?G?points
%?h:?threshold
%?y:?estimated?sourses
%?A:?estimated?mix?matrix

%?here?we?just?consider?the?special?casei.e?m?=?2
[m?T]?=?size（X）;
figure（‘Name‘‘guance‘）;
plot（X（1）X（2）‘.‘）;
if?nargin?d?=?round（0.15*L）*2;?%?the?hop?distance
overlap?=?L?-?d;?%?number?of?samples?of?overlap?between?adjacent?windows
w?=?hann（L）‘;?%?Hann?（Hanning）??window?function;
frame_X??=?bss_make_frames（Xwoverlap）;?%?decompose?X?into?frames.?For?instance?frame_X（::1）
%?correspond?to?1st?sensoreach?row?is?a?frame.

%?now?each?column?of?frame_X（::i）?is?a?frame?for?convenience?of?fft?operation
for?i=1:m
????frame_X_temp（::i）?=?frame_X（::i）‘;
end
frame_X?=?frame_X_temp;
clear?frame_X_temp;

frame_X_Fs?=?fft（frame_X）;

K?=?L/2?+1;?%?preserve?the?positive?half?spectrum
for?i?=?1:m
????temp_Matrix?=?frame_X_Fs（1:K:i）;
????realPart?=?real（temp_Matrix）;
????imagPart?=?imag（temp_Matrix）;
????temp_Matrix?=?[realPart;imagPart];
????[rowcolumn]?=?size（temp_Matrix）;
????Xu（i:）?=?reshape（temp_Matrix?1row*column）;
end

if?nargin?if?nargin?%?we?consider?the?special?case?for?m?=?2
theta?=?rem（atan2（Xu（2:）Xu（1:））+2*pipi）;
radius?=?sqrt（（Xu（1:）.*Xu（1:）+Xu（2:）.*Xu（2:）））;
radius?=?radius?/max（radius）;?%?normalize?to?one
theta_k?=?pi/2/G?+?（1:G）*pi/G;

if?nargin?index?=?find（radius>=h）;
radius?=?radius（index）;
theta?=?theta（index）;

figure（‘Name‘‘Scatter?Plot?‘）;
polar（thetaradius‘*‘）;

for?k?=?1:G
????potential（k）?=?sum（radius.*Tao（langda*（theta-theta_k（k））））;
end
figure（‘Name‘‘Potential?Funtction‘）;
plot（theta_k/pi*180potential）;

%????????A?point?is?considered?a?maximum?peak?if?it?has?the?maximal
%????????value?and?was?preceded?（to?the?left）?by?a?value?lower?by
%????????DELTA.
if?nargin?maxtab?=?peakdet（potential?delta?theta_k）;?%?find?the?maxima?of?potential?function
theta_esti?=?maxtab（:1）;
%?get?the?first?m?maxima?of?potential?function
theta_esti?=?sort（theta_esti‘descend‘）;
theta_esti?=?theta_esti（1:m）;
A?=?[cos（theta_esti）?sin（theta_esti）]‘;
W?=?inv（A）;?%?separation?matrix
y?=?W*X;
figure（‘Name‘‘source?singal‘）;
plot（y（1）y（2）‘.‘）;
end



%%
%?------------------------------PEAKDET.m--------------------------------

function?[maxtab?mintab]=peakdet（v?delta?x）
%PEAKDET?Detect?peaks?in?a?vector
%????????[MAXTAB?MINTAB]?=?PEAKDET（V?DELTA）?finds?the?local
%????????maxima?and?minima?（“peaks“）?in?the?vector?V.
%????????MAX