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。
h.c<A{[I6c u2K{3+r`' function FF=frft_PXJ(N,alpha);
k$kq| %matrix
2%0zPflT % FF is the kernel matrix of fractional Fourier transform
r$=MBeT % \copyright: zjliu
`we2zT % Author's email:
zjliu2001@163.com lZCvH1&" Ts=sqrt(2*pi/N); t=-(N-1)/2:(N-1)/2; t=t'; t=t*Ts;
.!0),KmkK variance=N/2/pi; HH=zeros(N); HH(:,1)=1; HH(:,2)=2*t;
vC~];!^ for k=3:N;
VVeO>j d HH(:,k)=HH(:,k-1).*t*2-2*(k-2)*HH(:,k-2);
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end
I1U {t HH(:,1)=1/sqrt(sqrt(variance))*HH(:,1).*exp(-t.*t/2);
x!bFbi#!" for k=2:N;
+U&aK dQs HH(:,k)=exp(-t.*t/2).*HH(:,k)/sqrt(2.^(k-1)*...
<lZyUd factorial(k-1)*sqrt(variance));
(:E_m|00; end
e:{v.C0ez if mod(N,2)==1;
Vnuz!
6. W=0:N-1; k=exp(-i*alpha*W); D=diag(k);
ju8tNL,J else
I=l() ET= W=0:N-2; W=cat(2,W,[N]); k=exp(-i*alpha*W); D=diag(k);
i;xH end
aB<~T[H%h FF=Ts*HH*D*HH'*2;
tu6oa[s % Reference:
p3 I{ % by 平先军.一种新的分数阶傅立叶变换快速算法.电子学报.
b!SGQv(^M % 2001(3),Vol.29:406-408.