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。
[qUN 4x5b #6Fez`A function FF=frft_PXJ(N,alpha);
`nM/l@ %matrix
^bg2[FV % FF is the kernel matrix of fractional Fourier transform
-}O1dEn. % \copyright: zjliu
voP7"Dl[ % Author's email:
zjliu2001@163.com ('wY9kvL& Ts=sqrt(2*pi/N); t=-(N-1)/2:(N-1)/2; t=t'; t=t*Ts;
<h%O?mkC variance=N/2/pi; HH=zeros(N); HH(:,1)=1; HH(:,2)=2*t;
f=C ,e/sw for k=3:N;
AjcX N HH(:,k)=HH(:,k-1).*t*2-2*(k-2)*HH(:,k-2);
;<yd^Xs end
m8'C_U^89 HH(:,1)=1/sqrt(sqrt(variance))*HH(:,1).*exp(-t.*t/2);
:I -V_4b for k=2:N;
`>0MNmu HH(:,k)=exp(-t.*t/2).*HH(:,k)/sqrt(2.^(k-1)*...
fkf1m:Ckh factorial(k-1)*sqrt(variance));
\^ghdU end
*.L81er5~ if mod(N,2)==1;
N\:.
M W=0:N-1; k=exp(-i*alpha*W); D=diag(k);
-F'b8:m else
"k]CW\H6z W=0:N-2; W=cat(2,W,[N]); k=exp(-i*alpha*W); D=diag(k);
<N\v)Ug` end
yjfat&$ FF=Ts*HH*D*HH'*2;
~ P~ % Reference:
u6>?AW1~ % by 平先军.一种新的分数阶傅立叶变换快速算法.电子学报.
}ci#> % 2001(3),Vol.29:406-408.