function?c?=?Fast_Kurtogram（xnlevelFsopt1opt2）
%?Fast_Kurtogram（xnlevelFs）
%?Computes?the?fast?kurtogram?of?signal?x?up?to?level?‘nlevel‘
%?Maximum?number?of?decomposition?levels?is?log2（length（x））?but?it?is?
%?recommended?to?stay?by?a?factor?1/8?below?this.
%?Fs?=?sampling?frequency?of?signal?x?（default?is?Fs?=?1）
%?opt1?=?1:?the?kurtogram?is?computed?via?a?fast?decimated?filterbank?tree
%?opt1?=?2:?the?kurtogram?is?computed?via?the?short-time?Fourier?transform
%?（if?there?is?any?difference?in?the?kurtogram?between?the?two?measures?this?is
%?due?to?the?presence?of?impulsive?additive?noise）
%?opt2?=?1:?classical?kurtosis?based?on?4th?order?statistics?
%?opt2?=?2:?robust?kurtosis?based?on?2nd?order?statistics?of?the?envelope
%?（option?1?is?faster?and?has?more?flexibility?than?option?2?in?the?design?of?the
%?analysis?filter:?a?short?filter?in?option?1?gives?virtually?the?same?results?as?option?2）
%
%?-------------------
%?J.?Antoni?:?02/2005
%?-------------------

N?=?length（x）;
N2?=?log2（N）?-?7;%最大允許分解層
if?nlevel?>?N2%判斷輸入分解層是否大于最大允許分解層
???error（‘Please?enter?a?smaller?number?of?decomposition?levels‘）;
end

if?nargin????opt2?=?input（‘Choose?the?kurtosis?measure?（classic?=?1?;?robust?=?2）:?‘）;
???if?nargin???????opt1??=?input（‘Choose?the?algorithm?（filterbank?=?1?;?stft-based?=?2）:?‘）;
??????if?nargin??????????Fs?=?1;
??????end
???end
?end

%?Fast?computation?of?the?kurtogram
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if?opt1?==?1
???%?1）?Filterbank-based?kurtogram
???%%%%%%%%%%%%%%%%%%%%%%%%%%%%
???%?Analytic?generating?filters
???N?=?16;			fc?=?.4;					%?a?short?filter?is?just?good?enough!
???h?=?fir1（Nfc）.*exp（2i*pi*（0:N）*.125）;%二分段低通濾波器
???n?=?2:N+1;
???g?=?h（1+mod（1-nN））.*（-1）.^（1-n）;%二分段高通濾波器
???%?
???N?=?fix（3/2*N）;
???h1?=?fir1（N2/3*fc）.*exp（2i*pi*（0:N）*.25/3）;%三分段第一段濾波器
???h2?=?h1.*exp（2i*pi*（0:N）/6）;%三分段第二段濾波器
???h3?=?h1.*exp（2i*pi*（0:N）/3）;%三分段第三段濾波器??
???%?
???if?opt2?==?1
??????Kwav?=?K_wpQ（xhgh1h2h3nlevel‘kurt2‘）;				%?kurtosis?of?the?complex?envelope
???else
??????Kwav?=?K_wpQ（xhgh1h2h3nlevel‘kurt1‘）;				%?variance?of?the?envelope?magnitude
???end
???Kwav?=?Kwav.*（Kwav>0）;												%?keep?positive?values?only!
???
else?
???%?2）?STFT-based?kurtogram
???%%%%%%%%%%%%%%%%%%%%%%%%%
???Nfft?=?2.^[3:nlevel+2];				%?level?1?of?wav_kurt?roughly?corresponds?to?a?4-sample?hanning?window?with?stft_kurt
???%											??or?a?8-sample?flattop	第一層分8段	
???temp?=?[3*Nfft（1）/2?3*Nfft（1:end-2）;Nfft（2:end）];%第一行為三分層段數(shù)，第二行為二分層段數(shù)
???Nfft?=?[Nfft（1）?temp（:）‘];%用矩陣計(jì)算而不是循環(huán)賦值的方法，所有分層段數(shù)
???if?opt2?==?1
??????Kstft?=?Kf_fft（xNfft1‘kurt2‘）;							%?kurtosis?of?the?complex?envelope
??????Kx?=?kurt（x‘kurt2‘）;%未分層前的信號(hào)峭度
???else
??????Kstft?=?Kf_fft（xNfft1‘kurt1‘）;							%?variance?of?the?envelope?magnitude
??????Kx?=?kurt（x‘kurt1‘）;
???end
???Kstft?=?[Kx*ones（1