function?[AS]=jade（Xm）
%?Source?separation?of?complex?signals?with?JADE.
%?Jade?performs?‘Source?Separation‘?in?the?following?sense:
%???X?is?an?n?x?T?data?matrix?assumed?modelled?as?X?=?A?S?+?N?where
%?
%?o?A?is?an?unknown?n?x?m?matrix?with?full?rank.
%?o?S?is?a?m?x?T?data?matrix?（source?signals）?with?the?properties
%????	a）?for?each?t?the?components?of?S（:t）?are?statistically
%????	???independent
%?	b）?for?each?p?the?S（p:）?is?the?realization?of?a?zero-mean
%?	???‘source?signal‘.
%?	c）?At?most?one?of?these?processes?has?a?vanishing?4th-order
%?	???cumulant.
%?o??N?is?a?n?x?T?matrix.?It?is?a?realization?of?a?spatially?white
%????Gaussian?noise?i.e.?Cov（X）?=?sigma*eye（n）?with?unknown?variance
%????sigma.??This?is?probably?better?than?no?modeling?at?all...
%
%?Jade?performs?source?separation?via?a?
%?Joint?Approximate?Diagonalization?of?Eigen-matrices.??
%
%?THIS?VERSION?ASSUMES?ZERO-MEAN?SIGNALS
%
%?Input?:
%???*?X:?Each?column?of?X?is?a?sample?from?the?n?sensors
%???*?m:?m?is?an?optional?argument?for?the?number?of?sources.
%?????If?ommited?JADE?assumes?as?many?sources?as?sensors.
%
%?Output?:
%????*?A?is?an?n?x?m?estimate?of?the?mixing?matrix
%????*?S?is?an?m?x?T?naive?（ie?pinv（A）*X）??estimate?of?the?source?signals
%
%
%?Version?1.5.??Copyright:?JF?Cardoso.??
%
%?See?notes?references?and?revision?history?at?the?bottom?of?this?file



[nT]	=?size（X）;

%%??source?detection?not?implemented?yet?!
if?nargin==1?m=n?;?end;


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%?A?few?parameters?that?could?be?adjusted
nem	=?m;		%?number?of?eigen-matrices?to?be?diagonalized
seuil	=?1/sqrt（T）/100;%?a?statistical?threshold?for?stopping?joint?diag


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%?whitening
%
if?m?	[UD]?	=?eig（（X*X‘）/T）;?
	[puissk]=sort（diag（D））;
?	ibl?	=?sqrt（puiss（n-m+1:n）-mean（puiss（1:n-m）））;
?	bl?	=?ones（m1）?./?ibl?;
?	W	=?diag（bl）*U（1:nk（n-m+1:n））‘;
?	IW?	=?U（1:nk（n-m+1:n））*diag（ibl）;
else????%assumes?no?noise
?	IW?	=?sqrtm（（X*X‘）/T）;
?	W	=?inv（IW）;
end;
Y	=?W*X;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%?Cumulant?estimation


R	=?（Y*Y‘?）/T?;
C	=?（Y*Y.‘）/T?;

Yl	=?zeros（1T）;
Ykl	=?zeros（1T）;
Yjkl	=?zeros（1T）;

Q	=?zeros（m*m*m*m1）?;
index	=?1;

for?lx?=?1:m?;?Yl?	=?Y（lx:）;
for?kx?=?1:m?;?Ykl?	=?Yl.*conj（Y（kx:））;
for?jx?=?1:m?;?Yjkl	=?Ykl.*conj（Y（jx:））;
for?ix?=?1:m?;?
	Q（index）?=?...
	（Yjkl?*?Y（ix:）.‘）/T?-??R（ixjx）*R（lxkx）?-??R（ixkx）*R（lxjx）?-??C（ixlx）*conj（C（jxkx））??;
	index	=?index?+?1?;
end?;
end?;
end?;
end

%%?If?you?prefer?to?use?more?memory?and?less?CPU?you?may?prefer?this
%%?code?（due?to?J.?Galy?of?ENSICA）?for?the?estimation?the?cumulants
%ones_m?=?ones（m1）?;?
%T1?	=?kron（ones_mY）;?
%T2?	=?kron（Yones_m）;??
%TT?	=?（T1.*?conj（T2））?;
%TS?	=?（T1?*?T2.‘）/T?;
%R?	=?（Y*Y‘）/T??;
%Q	=?（TT*TT‘）/T?-?kron（Rones（m））.*kron（ones