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。
|++\"g 7dtkylW function FF=frft_PXJ(N,alpha);
}>< v7 %matrix
#jd&f,Tt % FF is the kernel matrix of fractional Fourier transform
&_W~d0 % \copyright: zjliu
x4%1P w % Author's email:
zjliu2001@163.com ;kb);iT Ts=sqrt(2*pi/N); t=-(N-1)/2:(N-1)/2; t=t'; t=t*Ts;
vG'I|OWg variance=N/2/pi; HH=zeros(N); HH(:,1)=1; HH(:,2)=2*t;
5><KTya?= for k=3:N;
c%vtg.A HH(:,k)=HH(:,k-1).*t*2-2*(k-2)*HH(:,k-2);
q>Kzl/~c.P end
Z,}c) HH(:,1)=1/sqrt(sqrt(variance))*HH(:,1).*exp(-t.*t/2);
kYnp$8 for k=2:N;
WI}cXXUKm0 HH(:,k)=exp(-t.*t/2).*HH(:,k)/sqrt(2.^(k-1)*...
}`^DO
Ar factorial(k-1)*sqrt(variance));
3T84f[CFJ end
6&s"
"J)3 if mod(N,2)==1;
$s"{C"4q W=0:N-1; k=exp(-i*alpha*W); D=diag(k);
cPbAR' else
QP:|D_k W=0:N-2; W=cat(2,W,[N]); k=exp(-i*alpha*W); D=diag(k);
L wP end
A8U\/GP FF=Ts*HH*D*HH'*2;
~x6<A\ % Reference:
G e+T[ % by 平先军.一种新的分数阶傅立叶变换快速算法.电子学报.
f S-PM3 % 2001(3),Vol.29:406-408.