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。
/B$"fxFf ,x| 4nk_ function FF=frft_PXJ(N,alpha);
v;S7i>\ %matrix
>EFjyhVE % FF is the kernel matrix of fractional Fourier transform
~jab/cR % \copyright: zjliu
<RmI)g>'_^ % Author's email:
zjliu2001@163.com |x|#n Ts=sqrt(2*pi/N); t=-(N-1)/2:(N-1)/2; t=t'; t=t*Ts;
vUGEzC M variance=N/2/pi; HH=zeros(N); HH(:,1)=1; HH(:,2)=2*t;
3~"G(UP for k=3:N;
r5qp[Ss3F HH(:,k)=HH(:,k-1).*t*2-2*(k-2)*HH(:,k-2);
aOq>Ra{T end
+OFq=M HH(:,1)=1/sqrt(sqrt(variance))*HH(:,1).*exp(-t.*t/2);
n*6 b*fl for k=2:N;
+/60$60[z HH(:,k)=exp(-t.*t/2).*HH(:,k)/sqrt(2.^(k-1)*...
n'D1s:W^B factorial(k-1)*sqrt(variance));
:CO>g=` end
{g?$u if mod(N,2)==1;
+'abAST
t W=0:N-1; k=exp(-i*alpha*W); D=diag(k);
4P@Ak7iL(V else
&?mH[rG" W=0:N-2; W=cat(2,W,[N]); k=exp(-i*alpha*W); D=diag(k);
8\m_.e end
\*x]xc/^ FF=Ts*HH*D*HH'*2;
B./Lp_QK % Reference:
Vx@JP93| % by 平先军.一种新的分数阶傅立叶变换快速算法.电子学报.
^)&d7cSc % 2001(3),Vol.29:406-408.