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。
meV Z_f/ Z+U -+eG function FF=frft_PXJ(N,alpha);
}G{"Mp4 %matrix
dF51_Kk % FF is the kernel matrix of fractional Fourier transform
&1T)'Bn % \copyright: zjliu
Brs6RkRf % Author's email:
zjliu2001@163.com o?/H<k\5 Ts=sqrt(2*pi/N); t=-(N-1)/2:(N-1)/2; t=t'; t=t*Ts;
d.w]\ variance=N/2/pi; HH=zeros(N); HH(:,1)=1; HH(:,2)=2*t;
g#74c'+ for k=3:N;
;\A_-a_(# HH(:,k)=HH(:,k-1).*t*2-2*(k-2)*HH(:,k-2);
KNN{2thy ` end
Ig!0A}f HH(:,1)=1/sqrt(sqrt(variance))*HH(:,1).*exp(-t.*t/2);
)=gU~UV for k=2:N;
A/a=)su HH(:,k)=exp(-t.*t/2).*HH(:,k)/sqrt(2.^(k-1)*...
,S
dj"C factorial(k-1)*sqrt(variance));
H0OO+MCe end
)b]!IP3 if mod(N,2)==1;
[[T6X9 W=0:N-1; k=exp(-i*alpha*W); D=diag(k);
YBj*c$.D0 else
l*hWws[ W=0:N-2; W=cat(2,W,[N]); k=exp(-i*alpha*W); D=diag(k);
L
/ PAC end
7=yM40 FF=Ts*HH*D*HH'*2;
;|XX^ % Reference:
aTm R~k % by 平先军.一种新的分数阶傅立叶变换快速算法.电子学报.
{Lv"wec*x % 2001(3),Vol.29:406-408.