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。
^^kL.C Ym naiy] oY" function FF=frft_PXJ(N,alpha);
~09k IO) %matrix
o0#zk % FF is the kernel matrix of fractional Fourier transform
^y2}C$1V % \copyright: zjliu
drd5oZ % Author's email:
zjliu2001@163.com n~'cKy)m Ts=sqrt(2*pi/N); t=-(N-1)/2:(N-1)/2; t=t'; t=t*Ts;
*#; variance=N/2/pi; HH=zeros(N); HH(:,1)=1; HH(:,2)=2*t;
an,JV0 for k=3:N;
qd@Fb* HH(:,k)=HH(:,k-1).*t*2-2*(k-2)*HH(:,k-2);
7da~+(yhr end
R7ExMJw HH(:,1)=1/sqrt(sqrt(variance))*HH(:,1).*exp(-t.*t/2);
#(1R:z\: for k=2:N;
.(X!*J]G HH(:,k)=exp(-t.*t/2).*HH(:,k)/sqrt(2.^(k-1)*...
yCZ[z
A factorial(k-1)*sqrt(variance));
Gn>~CoFN end
9}#9i^%} if mod(N,2)==1;
GpGq' 8|( W=0:N-1; k=exp(-i*alpha*W); D=diag(k);
ldNWdz else
VCc57Bo W=0:N-2; W=cat(2,W,[N]); k=exp(-i*alpha*W); D=diag(k);
,Laz515 end
;-d2~1$ FF=Ts*HH*D*HH'*2;
YfJQ]tt1 % Reference:
7YQ689"J6B % by 平先军.一种新的分数阶傅立叶变换快速算法.电子学报.
!= u
S % 2001(3),Vol.29:406-408.