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。
pJ1\@G ^ZS!1%1 function FF=frft_PXJ(N,alpha);
$'eY-U8q %matrix
\JR^uJ{Y % FF is the kernel matrix of fractional Fourier transform
"Lk BN0D % \copyright: zjliu
[lSQMoi3 % Author's email:
zjliu2001@163.com d)Z&_v<| Ts=sqrt(2*pi/N); t=-(N-1)/2:(N-1)/2; t=t'; t=t*Ts;
L[nDjQn" variance=N/2/pi; HH=zeros(N); HH(:,1)=1; HH(:,2)=2*t;
m`$Q/SyvG for k=3:N;
n`w]? bL HH(:,k)=HH(:,k-1).*t*2-2*(k-2)*HH(:,k-2);
4e|N^h*! end
0J466H_d{ HH(:,1)=1/sqrt(sqrt(variance))*HH(:,1).*exp(-t.*t/2);
[Pjitw/? for k=2:N;
[MbbL HH(:,k)=exp(-t.*t/2).*HH(:,k)/sqrt(2.^(k-1)*...
Np$&8v+en factorial(k-1)*sqrt(variance));
1\aTA, end
iV#A-9 if mod(N,2)==1;
\Z42EnJ W=0:N-1; k=exp(-i*alpha*W); D=diag(k);
)'RaMo` 4 else
?fC9)s W=0:N-2; W=cat(2,W,[N]); k=exp(-i*alpha*W); D=diag(k);
9MI9$s2y end
8L_OH FF=Ts*HH*D*HH'*2;
]i0=3H2 % Reference:
O8"
t.W % by 平先军.一种新的分数阶傅立叶变换快速算法.电子学报.
0&Ftx%6% % 2001(3),Vol.29:406-408.