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。
x 3co? 2uR4~XjF function FF=frft_PXJ(N,alpha);
A)a+LW'=u %matrix
LYT<o FE- % FF is the kernel matrix of fractional Fourier transform
iC0,zk4 & % \copyright: zjliu
V'h z1roe % Author's email:
zjliu2001@163.com #w?%&,Kp Ts=sqrt(2*pi/N); t=-(N-1)/2:(N-1)/2; t=t'; t=t*Ts;
A(sx5Ynp variance=N/2/pi; HH=zeros(N); HH(:,1)=1; HH(:,2)=2*t;
5Fm?,^ for k=3:N;
nk,Mo5iqV HH(:,k)=HH(:,k-1).*t*2-2*(k-2)*HH(:,k-2);
n[S*gX0 end
..{^"`FQ HH(:,1)=1/sqrt(sqrt(variance))*HH(:,1).*exp(-t.*t/2);
5+"8q#X$ for k=2:N;
_q4dgi z HH(:,k)=exp(-t.*t/2).*HH(:,k)/sqrt(2.^(k-1)*...
{[y"]_B4 factorial(k-1)*sqrt(variance));
$zA[5}{ZtQ end
jN{xpd if mod(N,2)==1;
X10TZ W=0:N-1; k=exp(-i*alpha*W); D=diag(k);
{ZI6!zh' else
Vw@x W=0:N-2; W=cat(2,W,[N]); k=exp(-i*alpha*W); D=diag(k);
;j\$[4W.i end
h pes FF=Ts*HH*D*HH'*2;
%z_b/yG % Reference:
Kyiez]T6%q % by 平先军.一种新的分数阶傅立叶变换快速算法.电子学报.
KFG^vmrn % 2001(3),Vol.29:406-408.