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。
Tr?p/9.m
V48_aL function FF=frft_PXJ(N,alpha);
li%@HdA! %matrix
*O$|,EsY % FF is the kernel matrix of fractional Fourier transform
8xlj,}QO\ % \copyright: zjliu
OL\-SQ& % Author's email:
zjliu2001@163.com A$wC!P|; Ts=sqrt(2*pi/N); t=-(N-1)/2:(N-1)/2; t=t'; t=t*Ts;
AW r2Bv variance=N/2/pi; HH=zeros(N); HH(:,1)=1; HH(:,2)=2*t;
^|MS2' for k=3:N;
`<tRfl}qs HH(:,k)=HH(:,k-1).*t*2-2*(k-2)*HH(:,k-2);
C|]c#X2t3 end
E{V?[HcWq HH(:,1)=1/sqrt(sqrt(variance))*HH(:,1).*exp(-t.*t/2);
51ViJdZ for k=2:N;
bhUE!h< HH(:,k)=exp(-t.*t/2).*HH(:,k)/sqrt(2.^(k-1)*...
V=ll 9M factorial(k-1)*sqrt(variance));
}Q`+hJ0 end
t`6]eRR if mod(N,2)==1;
(3N/DY1/ W=0:N-1; k=exp(-i*alpha*W); D=diag(k);
Z RjM^
d; else
Q9cSrU[$ W=0:N-2; W=cat(2,W,[N]); k=exp(-i*alpha*W); D=diag(k);
3N > V
sl end
Qb^{` FF=Ts*HH*D*HH'*2;
Sd6O?&( % Reference:
0gqV>: % by 平先军.一种新的分数阶傅立叶变换快速算法.电子学报.
- egTZW- % 2001(3),Vol.29:406-408.