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。
#!p=P<4M
L'{;V\d function FF=frft_PXJ(N,alpha);
y e!Bfz> %matrix
F\1nc"K/( % FF is the kernel matrix of fractional Fourier transform
zx^]3} % \copyright: zjliu
kTQ:k
}%B % Author's email:
zjliu2001@163.com b ABx'E Ts=sqrt(2*pi/N); t=-(N-1)/2:(N-1)/2; t=t'; t=t*Ts;
H"(:6
` variance=N/2/pi; HH=zeros(N); HH(:,1)=1; HH(:,2)=2*t;
3nuf3) for k=3:N;
M ,V+bt HH(:,k)=HH(:,k-1).*t*2-2*(k-2)*HH(:,k-2);
.d`+#1Ot( end
${'gyD HH(:,1)=1/sqrt(sqrt(variance))*HH(:,1).*exp(-t.*t/2);
pTq,"}J!+ for k=2:N;
\V@SCA' HH(:,k)=exp(-t.*t/2).*HH(:,k)/sqrt(2.^(k-1)*...
rUfW0 factorial(k-1)*sqrt(variance));
A2' end
\C.%S +u if mod(N,2)==1;
zi:F/TlUC W=0:N-1; k=exp(-i*alpha*W); D=diag(k);
q0WW^jwQ else
BmYU#h W=0:N-2; W=cat(2,W,[N]); k=exp(-i*alpha*W); D=diag(k);
;ak3@Uee end
J<DV7zV FF=Ts*HH*D*HH'*2;
Wu)ATs} % Reference:
xrx{8pf % by 平先军.一种新的分数阶傅立叶变换快速算法.电子学报.
|)6(_7e9 % 2001(3),Vol.29:406-408.