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。
<g3)!VR^q ,C97|6rC function FF=frft_PXJ(N,alpha);
NcMohpkq %matrix
0tb%h[%,M % FF is the kernel matrix of fractional Fourier transform
RJhafUJ zH % \copyright: zjliu
d.Im{-S % Author's email:
zjliu2001@163.com IF~E; Ts=sqrt(2*pi/N); t=-(N-1)/2:(N-1)/2; t=t'; t=t*Ts;
R;l;;dC= variance=N/2/pi; HH=zeros(N); HH(:,1)=1; HH(:,2)=2*t;
K~6,xZlDWM for k=3:N;
bbe$6x wi HH(:,k)=HH(:,k-1).*t*2-2*(k-2)*HH(:,k-2);
1r?hRJ:' end
vmsrypm HH(:,1)=1/sqrt(sqrt(variance))*HH(:,1).*exp(-t.*t/2);
734f&2 for k=2:N;
2>+(OL4l HH(:,k)=exp(-t.*t/2).*HH(:,k)/sqrt(2.^(k-1)*...
b<bj5m4fz> factorial(k-1)*sqrt(variance));
s:ZYiZ- end
Q}6!t$Vk if mod(N,2)==1;
@]F1J W=0:N-1; k=exp(-i*alpha*W); D=diag(k);
h'm-]v else
xP+`scv*m# W=0:N-2; W=cat(2,W,[N]); k=exp(-i*alpha*W); D=diag(k);
xmXuBp:M(R end
rZ#ZY FF=Ts*HH*D*HH'*2;
3LW_qX % Reference:
{'@`:p&3r % by 平先军.一种新的分数阶傅立叶变换快速算法.电子学报.
Qo$j'|lD % 2001(3),Vol.29:406-408.