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。
vO
3-B s $?u'}G3 function FF=frft_PXJ(N,alpha);
SrT=XX, %matrix
E/Adi^ % FF is the kernel matrix of fractional Fourier transform
A4IPd % \copyright: zjliu
b|-7EI>l9 % Author's email:
zjliu2001@163.com jlM%Y
ZC Ts=sqrt(2*pi/N); t=-(N-1)/2:(N-1)/2; t=t'; t=t*Ts;
rhH !-`m variance=N/2/pi; HH=zeros(N); HH(:,1)=1; HH(:,2)=2*t;
ApotRr$) for k=3:N;
qG8-UOUDt HH(:,k)=HH(:,k-1).*t*2-2*(k-2)*HH(:,k-2);
+V,Ld&r end
}Zp5d7(@w HH(:,1)=1/sqrt(sqrt(variance))*HH(:,1).*exp(-t.*t/2);
V5up/ 6b,1 for k=2:N;
MngfXm HH(:,k)=exp(-t.*t/2).*HH(:,k)/sqrt(2.^(k-1)*...
"SFs\] Z factorial(k-1)*sqrt(variance));
wpepi8w, end
`XK+Y if mod(N,2)==1;
^!x}e+ o W=0:N-1; k=exp(-i*alpha*W); D=diag(k);
VCCG_K9' else
g6!#n W=0:N-2; W=cat(2,W,[N]); k=exp(-i*alpha*W); D=diag(k);
M^?=!!US^ end
L.$+W} FF=Ts*HH*D*HH'*2;
40Z/;,wp{ % Reference:
Jh`6@d % by 平先军.一种新的分数阶傅立叶变换快速算法.电子学报.
^SJa/I EZ. % 2001(3),Vol.29:406-408.