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。
jR mo9Bb2 bxF'`^En function FF=frft_PXJ(N,alpha);
a3E.rr;b %matrix
_[ufH* % FF is the kernel matrix of fractional Fourier transform
#P-T4R % \copyright: zjliu
($^=f }+ % Author's email:
zjliu2001@163.com vS+E`[ Ts=sqrt(2*pi/N); t=-(N-1)/2:(N-1)/2; t=t'; t=t*Ts;
$|!@$A j variance=N/2/pi; HH=zeros(N); HH(:,1)=1; HH(:,2)=2*t;
h<IPV'1 for k=3:N;
1A;f[Rze HH(:,k)=HH(:,k-1).*t*2-2*(k-2)*HH(:,k-2);
qZ DP- end
CC{{@
HH(:,1)=1/sqrt(sqrt(variance))*HH(:,1).*exp(-t.*t/2);
8z'_dfP=5 for k=2:N;
qgZN&7Nn: HH(:,k)=exp(-t.*t/2).*HH(:,k)/sqrt(2.^(k-1)*...
!ZTBiC5R factorial(k-1)*sqrt(variance));
#H/suQZN"g end
(eF "[,z if mod(N,2)==1;
xC.Tipn> W=0:N-1; k=exp(-i*alpha*W); D=diag(k);
f|-%., else
\TTt!"aK W=0:N-2; W=cat(2,W,[N]); k=exp(-i*alpha*W); D=diag(k);
/&g~*AL end
G}p*oz~ FF=Ts*HH*D*HH'*2;
CxJkT2 % Reference:
>p@v'h/Cr % by 平先军.一种新的分数阶傅立叶变换快速算法.电子学报.
'AJlkLqm#> % 2001(3),Vol.29:406-408.