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。
d:6?miMH]t rm NqS+t function FF=frft_PXJ(N,alpha);
eW]K~SPd7 %matrix
T"XP`gk % FF is the kernel matrix of fractional Fourier transform
:grJ}i-D % \copyright: zjliu
{
D1. % Author's email:
zjliu2001@163.com "EQ-`b=I4 Ts=sqrt(2*pi/N); t=-(N-1)/2:(N-1)/2; t=t'; t=t*Ts;
b}p 0&%I variance=N/2/pi; HH=zeros(N); HH(:,1)=1; HH(:,2)=2*t;
hp!UW for k=3:N;
XS]=sfN HH(:,k)=HH(:,k-1).*t*2-2*(k-2)*HH(:,k-2);
VC\43A,9 end
GmB7@-[QA% HH(:,1)=1/sqrt(sqrt(variance))*HH(:,1).*exp(-t.*t/2);
yK<%AV@v for k=2:N;
pIk&NI HH(:,k)=exp(-t.*t/2).*HH(:,k)/sqrt(2.^(k-1)*...
^S'}RZ*> factorial(k-1)*sqrt(variance));
c.Pyt end
,YJ\
$? if mod(N,2)==1;
>z1RCQWju W=0:N-1; k=exp(-i*alpha*W); D=diag(k);
/+ vl({vV else
iK1<4) W=0:N-2; W=cat(2,W,[N]); k=exp(-i*alpha*W); D=diag(k);
HiEXw}Hkz end
[L8Bgw1 FF=Ts*HH*D*HH'*2;
!MNUp(: % Reference:
v&%GK5j7O % by 平先军.一种新的分数阶傅立叶变换快速算法.电子学报.
xCD|UC46?X % 2001(3),Vol.29:406-408.