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。
`1lGAKv AH:0h X6+ function FF=frft_PXJ(N,alpha);
:xY9eq= %matrix
ROO@EQ#`Z % FF is the kernel matrix of fractional Fourier transform
TrQUhmS/! % \copyright: zjliu
T5dnj&N ] % Author's email:
zjliu2001@163.com [7,q@>:CS Ts=sqrt(2*pi/N); t=-(N-1)/2:(N-1)/2; t=t'; t=t*Ts;
NFqGbA| variance=N/2/pi; HH=zeros(N); HH(:,1)=1; HH(:,2)=2*t;
L08lkq, for k=3:N;
3MDs?qx>s HH(:,k)=HH(:,k-1).*t*2-2*(k-2)*HH(:,k-2);
lnK#q.] end
!bCaDTz HH(:,1)=1/sqrt(sqrt(variance))*HH(:,1).*exp(-t.*t/2);
C>QWV[F for k=2:N;
k=O HH(:,k)=exp(-t.*t/2).*HH(:,k)/sqrt(2.^(k-1)*...
vz&88jt factorial(k-1)*sqrt(variance));
_
Ewkb end
O0eM*~zI if mod(N,2)==1;
c IPOI'3d W=0:N-1; k=exp(-i*alpha*W); D=diag(k);
\Qf2:[-V0 else
xrv0% W=0:N-2; W=cat(2,W,[N]); k=exp(-i*alpha*W); D=diag(k);
VL|Z+3L end
@E>I<j,D FF=Ts*HH*D*HH'*2;
Mt@Ma ]! % Reference:
/<"ok;Pu7 % by 平先军.一种新的分数阶傅立叶变换快速算法.电子学报.
/Zxq-9
% 2001(3),Vol.29:406-408.