function?y=sgsmooth（xwidthorder）

%???A?smooth?method?first?mentioned?by?Savitzky?and?Golay?in?the?paper
%???Abraham?Savitzky?&?Marcel?J.?E.?Golay.?Smoothing?and?Differentiation?of?Data?by?
%???Simplified?Least?Squares?Procedures.?Analytical?Chemistry.196436（8）:1627-1639.
%???
%???Then?corrected?by?Jeans?Teinier?Yves?Termonia?&?Jules?Deltour?in?1972
%???published?by?Analytical?Chemistry?as?well.?And?Peter?A.?Gorry?in?his
%???article:?General?Least-Squares?Smoothing?and?Differentiation?by?the?Convolution?
%????????????（Savitzky-Golay）?Method?（Anal.Chem.199062（6）:?570-573）?showed?us?the
%???generalized?implementation?of?SG?least?square?smoothing?method.
%
%???The?algorithm?showed?in?this?program?mainly?from?Jeans?Ternier?etc.for?calculating?
%???the?weighting?parameters?also?from?Peter?A.?Gorry?for?calculating?the?leading?and?
%???trailing?value.Here?we?set?the?derivative?order?s=0.?
%???
%???y=SavGo（xwidthorder）:
%???x?----------?Data?you?must?input?and?it?must?be?a?vector.
%
%???width?------?The?window?width?for?smoothing.
%
%???order?------?The?order?of?polynomials.?It?must?be?smaller?than?the?window?width?you?
%????????????????choose?for?smooothing.
%
%???DNP.?2007.12.16

y=[];
[mn]=size（x）;

if?~any（[mn]==1）
????error（‘The?data?you?want?to?be?smoothed?should?be?a?vector!‘）;
????return
elseif?m==1
????x=x‘;??????????????%?Make?x?be?a?column?vector.
end

if?width<=order
????error（‘The?order?of?polynomials?must?be?smaller?then?the?window?width?you?choose!‘）;
????return
elseif?all（[width?order]<=0）
????error（‘The?window?width?and?order?must?be?positive!‘）;
????return
end

if?nargin?????error（‘You?must?input?data?for?smoothing?and?choose?the?window?width?and?polynomial?order.‘）;
????return
elseif?nargin?>?3
????error（‘Too?many?inputs!‘）;
????return
end

if?mod（width2）==0
????error（‘The?window?width?should?be?odd.‘）;
????return
end

m=（width-1）/2;
B=[];
h=zeros（width）;

%?Coefficient?matrix?................
for?i=-m:m
%?????for?t=-m:m
????????for?o=0:order
%?????????????coef=（（2*o+1）*factorial（2*m）/factorial（2*m-o））/（factorial（2*m+o+1）/factorial（2*m））;
%?????????????p_i=grampoly（iom）;
%?????????????p_t=grampoly（tom）;
%?????????????h（i+m+1t+m+1）=h（i+m+1t+m+1）+coef*p_i*p_t;
????????????B（i+m+1o+1）=i^o;
%?????????end
????end
end

%?^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
%?.........?Smoothing?data?..............

%?y=zeros（length（x）1）;
for?i=1:length（x）
????if?i-1-m?????????y（i）=h（:i）‘*x（1:2*m+1）;
????elseif?i?>?length（x）-m
????????y（i）=B（2*m+1-（length（x）-i）:）*（br\bq‘）*x（length（x）-2*m:end）;
????else
????????[bq?br]=qr（B0）;?????????%?QR?decomposition?of?B?for?Least?Square?Fitting.
????????y（i）=B（m+1:）*（br\bq‘）*x（i-m:i+m）;
????end
end
????????
????????
????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????
??

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----
?????文件????????3591??2007-12-26?21:11??sgsmooth.m