转载一个实现分数傅立叶变换的matlab程序，作者信息在程序中有。
,YEwz3$5u }bU1wIW9I function FF=frft_PXJ(N,alpha);
\yQs[l%J %matrix
anM]khs? % FF is the kernel matrix of fractional Fourier transform
+,"O#`sy< % \copyright: zjliu
!x%$xC^Iz % Author's email:
zjliu2001@163.com Q+Sx5JUR~ Ts=sqrt(2*pi/N); t=-(N-1)/2:(N-1)/2; t=t'; t=t*Ts;
12D>~#J variance=N/2/pi; HH=zeros(N); HH(:,1)=1; HH(:,2)=2*t;
kjS9?>i for k=3:N;
2 Nr * HH(:,k)=HH(:,k-1).*t*2-2*(k-2)*HH(:,k-2);
IB'gY0* end
E41ay:duAl HH(:,1)=1/sqrt(sqrt(variance))*HH(:,1).*exp(-t.*t/2);
iSiez' for k=2:N;
l\Q- - HH(:,k)=exp(-t.*t/2).*HH(:,k)/sqrt(2.^(k-1)*...
< Mt>v2a3Y factorial(k-1)*sqrt(variance));
|
Ns-l
(l end
^ UB *Q if mod(N,2)==1;
bu}N{cW W=0:N-1; k=exp(-i*alpha*W); D=diag(k);
n7CwGN% else
><l|&&e- W=0:N-2; W=cat(2,W,[N]); k=exp(-i*alpha*W); D=diag(k);
=>y%Aj&4 end
dKG 2f FF=Ts*HH*D*HH'*2;
8p91ni' % Reference:
HVG:q#=C % by 平先军.一种新的分数阶傅立叶变换快速算法.电子学报.
x{o&nhuk[S % 2001(3),Vol.29:406-408.
