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。
M`<D Z<:< Kq?7#,_ function FF=frft_PXJ(N,alpha);
~9c9@!RA2 %matrix
xn@jL;+<- % FF is the kernel matrix of fractional Fourier transform
btY Pp0o~ % \copyright: zjliu
5R Hs % Author's email:
zjliu2001@163.com 4Klfnki Ts=sqrt(2*pi/N); t=-(N-1)/2:(N-1)/2; t=t'; t=t*Ts;
X "0Q) variance=N/2/pi; HH=zeros(N); HH(:,1)=1; HH(:,2)=2*t;
ZJpI]^9| for k=3:N;
h>/ViB@"W| HH(:,k)=HH(:,k-1).*t*2-2*(k-2)*HH(:,k-2);
l}^#kHSyd end
0%t|?@HoN HH(:,1)=1/sqrt(sqrt(variance))*HH(:,1).*exp(-t.*t/2);
L8G4K) for k=2:N;
< D^x6{} HH(:,k)=exp(-t.*t/2).*HH(:,k)/sqrt(2.^(k-1)*...
; M(}fV] factorial(k-1)*sqrt(variance));
c 5;ROnTm end
3u^TJt ) if mod(N,2)==1;
ayD\b6Z2. W=0:N-1; k=exp(-i*alpha*W); D=diag(k);
%FU [ j^ else
-^5R51 W=0:N-2; W=cat(2,W,[N]); k=exp(-i*alpha*W); D=diag(k);
hmH$_YP} end
)yP> }ME FF=Ts*HH*D*HH'*2;
g)9/z % Reference:
M <)2 % 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#>J +QlG % 2001(3),Vol.29:406-408.
