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。
yl~_~<s6 X+aQ 7^"s function FF=frft_PXJ(N,alpha);
B={_}f %matrix
80*hi)ux[
% FF is the kernel matrix of fractional Fourier transform
cx$IWQf2 % \copyright: zjliu
);h(D!D, % Author's email:
zjliu2001@163.com @|SeabN^- Ts=sqrt(2*pi/N); t=-(N-1)/2:(N-1)/2; t=t'; t=t*Ts;
mkn1LzE|F variance=N/2/pi; HH=zeros(N); HH(:,1)=1; HH(:,2)=2*t;
din,yHu~ for k=3:N;
SlG v HH(:,k)=HH(:,k-1).*t*2-2*(k-2)*HH(:,k-2);
93HVx# end
N s +g9+<A HH(:,1)=1/sqrt(sqrt(variance))*HH(:,1).*exp(-t.*t/2);
y|}~"^+T for k=2:N;
&/? Ct!_ HH(:,k)=exp(-t.*t/2).*HH(:,k)/sqrt(2.^(k-1)*...
z6iKIw
$ factorial(k-1)*sqrt(variance));
F'Y ad end
c4Zpt%:}h if mod(N,2)==1;
X ha9x, W=0:N-1; k=exp(-i*alpha*W); D=diag(k);
I_ mus<sE else
JcR|{9ghT W=0:N-2; W=cat(2,W,[N]); k=exp(-i*alpha*W); D=diag(k);
Q?k*3A end
Ai<
beUS FF=Ts*HH*D*HH'*2;
=0=#M(w % Reference:
HrBJi % by 平先军.一种新的分数阶傅立叶变换快速算法.电子学报.
m}uOBR+ % 2001(3),Vol.29:406-408.