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。
hj=k[t|g} -5,+gakSk function FF=frft_PXJ(N,alpha);
@ [j%V ynf %matrix
j`_tb
% FF is the kernel matrix of fractional Fourier transform
)C$1)) % \copyright: zjliu
mJME1#j$/| % Author's email:
zjliu2001@163.com /D;cm Ts=sqrt(2*pi/N); t=-(N-1)/2:(N-1)/2; t=t'; t=t*Ts;
iy|xF~ variance=N/2/pi; HH=zeros(N); HH(:,1)=1; HH(:,2)=2*t;
6\6g-1B` for k=3:N;
,sltB3f HH(:,k)=HH(:,k-1).*t*2-2*(k-2)*HH(:,k-2);
{"\pMY'7 end
s,7OoLE HH(:,1)=1/sqrt(sqrt(variance))*HH(:,1).*exp(-t.*t/2);
be>KG ZU0 for k=2:N;
xhncQhf\ HH(:,k)=exp(-t.*t/2).*HH(:,k)/sqrt(2.^(k-1)*...
'o1lJ?~kH factorial(k-1)*sqrt(variance));
OQ4rJ#b end
F& ['w-n% if mod(N,2)==1;
"2`/mtMon W=0:N-1; k=exp(-i*alpha*W); D=diag(k);
bl4I4RB else
k j&hn W=0:N-2; W=cat(2,W,[N]); k=exp(-i*alpha*W); D=diag(k);
6V-JyTcxGI end
&}FWpo! FF=Ts*HH*D*HH'*2;
6' 9zpe@` % Reference:
u\=yY. % by 平先军.一种新的分数阶傅立叶变换快速算法.电子学报.
zO 6Sl[) % 2001(3),Vol.29:406-408.