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。
69[w/\ ,[+ZjAyG}# function FF=frft_PXJ(N,alpha);
Pau&4h0 %matrix
cM|af#o % FF is the kernel matrix of fractional Fourier transform
Uia)5z z8 % \copyright: zjliu
&xF4p,7 % Author's email:
zjliu2001@163.com BZ8h*|uT" Ts=sqrt(2*pi/N); t=-(N-1)/2:(N-1)/2; t=t'; t=t*Ts;
^?JEyY variance=N/2/pi; HH=zeros(N); HH(:,1)=1; HH(:,2)=2*t;
8'>.#vyMGv for k=3:N;
?yda.<"g9Y HH(:,k)=HH(:,k-1).*t*2-2*(k-2)*HH(:,k-2);
u~j'NOv end
W"#j7p`d HH(:,1)=1/sqrt(sqrt(variance))*HH(:,1).*exp(-t.*t/2);
9L UP{(uq for k=2:N;
Yf%[6Y{ HH(:,k)=exp(-t.*t/2).*HH(:,k)/sqrt(2.^(k-1)*...
axt6u)4%7: factorial(k-1)*sqrt(variance));
47$-5k30 end
a2IV!0x if mod(N,2)==1;
h?M'7Lti W=0:N-1; k=exp(-i*alpha*W); D=diag(k);
<L[ *hp else
'bd=,QW W=0:N-2; W=cat(2,W,[N]); k=exp(-i*alpha*W); D=diag(k);
Z.Lx^h+U end
ant-\w>} FF=Ts*HH*D*HH'*2;
V~tu<"% % Reference:
.oB'ttF1 % by 平先军.一种新的分数阶傅立叶变换快速算法.电子学报.
\:18Uoe7 % 2001(3),Vol.29:406-408.