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。
H6fR6Kr4j cx_.+ R function FF=frft_PXJ(N,alpha);
7E4Xvg+c %matrix
X.YMb
.\< % FF is the kernel matrix of fractional Fourier transform
Z#Q)a;RA % \copyright: zjliu
*Y!c6eA % Author's email:
zjliu2001@163.com W'0(0;+G/j Ts=sqrt(2*pi/N); t=-(N-1)/2:(N-1)/2; t=t'; t=t*Ts;
0qdgt variance=N/2/pi; HH=zeros(N); HH(:,1)=1; HH(:,2)=2*t;
Z3jtq-y for k=3:N;
O:^m#:[cE HH(:,k)=HH(:,k-1).*t*2-2*(k-2)*HH(:,k-2);
WZ#|?pJ end
BkO)hze HH(:,1)=1/sqrt(sqrt(variance))*HH(:,1).*exp(-t.*t/2);
Q|3SYJf for k=2:N;
~C;1}P%9x HH(:,k)=exp(-t.*t/2).*HH(:,k)/sqrt(2.^(k-1)*...
F~qiNV factorial(k-1)*sqrt(variance));
cag9f?w@V end
O7KR~d if mod(N,2)==1;
gJn_Z7Mg J W=0:N-1; k=exp(-i*alpha*W); D=diag(k);
_mi(:s( else
xQKD1#y W=0:N-2; W=cat(2,W,[N]); k=exp(-i*alpha*W); D=diag(k);
n-%8RV end
\q |n0> FF=Ts*HH*D*HH'*2;
ku`bwS % Reference:
HJV8P2f8` % by 平先军.一种新的分数阶傅立叶变换快速算法.电子学报.
#c2InwZV % 2001(3),Vol.29:406-408.