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。
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%Y function FF=frft_PXJ(N,alpha);
Z/*X)mBuB %matrix
U4.-{. % FF is the kernel matrix of fractional Fourier transform
8o7%qWX % \copyright: zjliu
HX`>"
?{ % Author's email:
zjliu2001@163.com >hFg,5 _l3 Ts=sqrt(2*pi/N); t=-(N-1)/2:(N-1)/2; t=t'; t=t*Ts;
B*-A erdH variance=N/2/pi; HH=zeros(N); HH(:,1)=1; HH(:,2)=2*t;
aGx[?}= for k=3:N;
C4h4W3w HH(:,k)=HH(:,k-1).*t*2-2*(k-2)*HH(:,k-2);
-LnNA`- end
{0IC2jE HH(:,1)=1/sqrt(sqrt(variance))*HH(:,1).*exp(-t.*t/2);
0;X0<IV for k=2:N;
@&F\ M} HH(:,k)=exp(-t.*t/2).*HH(:,k)/sqrt(2.^(k-1)*...
},& =r= B factorial(k-1)*sqrt(variance));
TNj WZ end
4f-I,)qCBk if mod(N,2)==1;
ixjhZk i< W=0:N-1; k=exp(-i*alpha*W); D=diag(k);
hlO,mU else
\)/dFo\l W=0:N-2; W=cat(2,W,[N]); k=exp(-i*alpha*W); D=diag(k);
:dML+R#Ymh end
h4,S/n FF=Ts*HH*D*HH'*2;
7.!`c-8
u % Reference:
rv26vnJy" % by 平先军.一种新的分数阶傅立叶变换快速算法.电子学报.
k0>]7t$L % 2001(3),Vol.29:406-408.