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。
15U=2j*.b ?e]4HHgU] function FF=frft_PXJ(N,alpha);
FNmIXpAn*@ %matrix
)_.@M '? % FF is the kernel matrix of fractional Fourier transform
F6Q #{Ufq % \copyright: zjliu
a%(1#2^`q! % Author's email:
zjliu2001@163.com x6,S#p Ts=sqrt(2*pi/N); t=-(N-1)/2:(N-1)/2; t=t'; t=t*Ts;
PU?kQZU~) variance=N/2/pi; HH=zeros(N); HH(:,1)=1; HH(:,2)=2*t;
MQ\:/]a for k=3:N;
r7ywK9UL HH(:,k)=HH(:,k-1).*t*2-2*(k-2)*HH(:,k-2);
sd8o&6 end
A7|"0*62 HH(:,1)=1/sqrt(sqrt(variance))*HH(:,1).*exp(-t.*t/2);
,Z>Rv Ll for k=2:N;
Uk;SY[mU HH(:,k)=exp(-t.*t/2).*HH(:,k)/sqrt(2.^(k-1)*...
^5,ASU factorial(k-1)*sqrt(variance));
"5dh]-m n end
@[
:s P if mod(N,2)==1;
!k<+-Lf:2 W=0:N-1; k=exp(-i*alpha*W); D=diag(k);
1P2%n[y else
:?RK>}4|F W=0:N-2; W=cat(2,W,[N]); k=exp(-i*alpha*W); D=diag(k);
/B1<N} end
%$]u6GKabi FF=Ts*HH*D*HH'*2;
sSD(mO<( % Reference:
7qW:^2y % by 平先军.一种新的分数阶傅立叶变换快速算法.电子学报.
uVscF
4 % 2001(3),Vol.29:406-408.