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。
Gx4uf ,-k?"|tQ function FF=frft_PXJ(N,alpha);
QZ7W:%r(4 %matrix
#n.v#FyNx % FF is the kernel matrix of fractional Fourier transform
%z[=T@ % \copyright: zjliu
IIXA)b! % Author's email:
zjliu2001@163.com !H c6$ Ts=sqrt(2*pi/N); t=-(N-1)/2:(N-1)/2; t=t'; t=t*Ts;
yHs9J1Sf variance=N/2/pi; HH=zeros(N); HH(:,1)=1; HH(:,2)=2*t;
yLXIjR for k=3:N;
pjV70D8$A HH(:,k)=HH(:,k-1).*t*2-2*(k-2)*HH(:,k-2);
Y:Lkh>S1Q end
]w]BKpU= HH(:,1)=1/sqrt(sqrt(variance))*HH(:,1).*exp(-t.*t/2);
H|j]uLZ for k=2:N;
?;5/"/i HH(:,k)=exp(-t.*t/2).*HH(:,k)/sqrt(2.^(k-1)*...
|pMP- factorial(k-1)*sqrt(variance));
P@5-3]m= end
Y Kp@n8A if mod(N,2)==1;
S7cD}yx*[ W=0:N-1; k=exp(-i*alpha*W); D=diag(k);
+9t{ovF?L else
rij%l+%@# W=0:N-2; W=cat(2,W,[N]); k=exp(-i*alpha*W); D=diag(k);
&+oJPpHi\ end
8(q8}s$> FF=Ts*HH*D*HH'*2;
F8tMZ,: % Reference:
VB8eGMo % by 平先军.一种新的分数阶傅立叶变换快速算法.电子学报.
asp\4-?$o % 2001(3),Vol.29:406-408.