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。
9>N\sOh XtCoX\da function FF=frft_PXJ(N,alpha);
.Y!;xB/ %matrix
LGIalf*7 % FF is the kernel matrix of fractional Fourier transform
QU:EY'2 % \copyright: zjliu
xC-BqVJ%_T % Author's email:
zjliu2001@163.com {Q)dU-\ Ts=sqrt(2*pi/N); t=-(N-1)/2:(N-1)/2; t=t'; t=t*Ts;
* [tc variance=N/2/pi; HH=zeros(N); HH(:,1)=1; HH(:,2)=2*t;
ZB828T3 for k=3:N;
i{8]'fM HH(:,k)=HH(:,k-1).*t*2-2*(k-2)*HH(:,k-2);
bE?'C h end
uie~' K\y HH(:,1)=1/sqrt(sqrt(variance))*HH(:,1).*exp(-t.*t/2);
%a5t15 9 for k=2:N;
On=u#DxQ HH(:,k)=exp(-t.*t/2).*HH(:,k)/sqrt(2.^(k-1)*...
dM Y
0 K factorial(k-1)*sqrt(variance));
Iz#yQ` end
Uz 0W <u3v if mod(N,2)==1;
#(6) ^ ( W=0:N-1; k=exp(-i*alpha*W); D=diag(k);
}2lO _i}L else
`dDa}b W=0:N-2; W=cat(2,W,[N]); k=exp(-i*alpha*W); D=diag(k);
"Y7+{ end
V1<ow'^i FF=Ts*HH*D*HH'*2;
7Rnm%8?T % Reference:
^IBGYl5n % by 平先军.一种新的分数阶傅立叶变换快速算法.电子学报.
j'+ELKQ % 2001(3),Vol.29:406-408.