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。
E7*]t_p"
e%qMrR function FF=frft_PXJ(N,alpha);
]{y ';MZ %matrix
5%W3&F6% % FF is the kernel matrix of fractional Fourier transform
N.VzA
6C % \copyright: zjliu
@P~u k % Author's email:
zjliu2001@163.com 9(H8MUF0{ Ts=sqrt(2*pi/N); t=-(N-1)/2:(N-1)/2; t=t'; t=t*Ts;
%;zA_Wg variance=N/2/pi; HH=zeros(N); HH(:,1)=1; HH(:,2)=2*t;
rL%xl,cn< for k=3:N;
?!
kup HH(:,k)=HH(:,k-1).*t*2-2*(k-2)*HH(:,k-2);
6L*y$e"Qc end
zZDr=6|r_ HH(:,1)=1/sqrt(sqrt(variance))*HH(:,1).*exp(-t.*t/2);
Tn-H8;Hg for k=2:N;
gHm^@ HH(:,k)=exp(-t.*t/2).*HH(:,k)/sqrt(2.^(k-1)*...
f[%iRfUFw factorial(k-1)*sqrt(variance));
@@I2bHyvb end
)JZfC&, if mod(N,2)==1;
}b+=, Sc" W=0:N-1; k=exp(-i*alpha*W); D=diag(k);
Ru
sa
&#[ else
B'=*92i>S W=0:N-2; W=cat(2,W,[N]); k=exp(-i*alpha*W); D=diag(k);
G&;W end
8HWY]:|oh FF=Ts*HH*D*HH'*2;
,>Yz1P)L % Reference:
N/y.=] % by 平先军.一种新的分数阶傅立叶变换快速算法.电子学报.
6b)1B\p % 2001(3),Vol.29:406-408.