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。
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P\A function FF=frft_PXJ(N,alpha);
\k?uh+xl %matrix
mmC&xZ5f % FF is the kernel matrix of fractional Fourier transform
P19nF[A % \copyright: zjliu
p"9a`/ % Author's email:
zjliu2001@163.com i#I+ Ts=sqrt(2*pi/N); t=-(N-1)/2:(N-1)/2; t=t'; t=t*Ts;
&V;^xMO! variance=N/2/pi; HH=zeros(N); HH(:,1)=1; HH(:,2)=2*t;
xpo<1Sr>S for k=3:N;
klC;fm2C HH(:,k)=HH(:,k-1).*t*2-2*(k-2)*HH(:,k-2);
5@3[t`n' end
imcq
H HH(:,1)=1/sqrt(sqrt(variance))*HH(:,1).*exp(-t.*t/2);
oiP8~ for k=2:N;
S4RvWTtQV HH(:,k)=exp(-t.*t/2).*HH(:,k)/sqrt(2.^(k-1)*...
0i}4T:J@` factorial(k-1)*sqrt(variance));
w_30g6tA end
/]=dPb% if mod(N,2)==1;
g?V>+oMx W=0:N-1; k=exp(-i*alpha*W); D=diag(k);
(eS/Q%ZGK else
K-Bf=7F, W=0:N-2; W=cat(2,W,[N]); k=exp(-i*alpha*W); D=diag(k);
>*ey 7g end
SJY<#_b FF=Ts*HH*D*HH'*2;
HJl$v#]#+ % Reference:
(17%/80-J % by 平先军.一种新的分数阶傅立叶变换快速算法.电子学报.
$~UQKv> % 2001(3),Vol.29:406-408.