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。
X;:qnnO hSkI]% function FF=frft_PXJ(N,alpha);
)T0%<(J %matrix
A$ 2 AYQ % FF is the kernel matrix of fractional Fourier transform
vNWCv % \copyright: zjliu
=#=<%HPT % Author's email:
zjliu2001@163.com 7 +]+S`p Ts=sqrt(2*pi/N); t=-(N-1)/2:(N-1)/2; t=t'; t=t*Ts;
X%X`o%AqC variance=N/2/pi; HH=zeros(N); HH(:,1)=1; HH(:,2)=2*t;
1F|e/h%^ for k=3:N;
vC#_PI HH(:,k)=HH(:,k-1).*t*2-2*(k-2)*HH(:,k-2);
=1ltX+
end
Budo9z_w HH(:,1)=1/sqrt(sqrt(variance))*HH(:,1).*exp(-t.*t/2);
h95a61a,Vy for k=2:N;
1Jm'9iy3 HH(:,k)=exp(-t.*t/2).*HH(:,k)/sqrt(2.^(k-1)*...
etw.l~y factorial(k-1)*sqrt(variance));
K x4_`;> end
t_xO-fT) if mod(N,2)==1;
^+J3E4 W=0:N-1; k=exp(-i*alpha*W); D=diag(k);
SHow~wxw else
%m/W4Nk W=0:N-2; W=cat(2,W,[N]); k=exp(-i*alpha*W); D=diag(k);
wn1` 9 end
p[LPi5 FF=Ts*HH*D*HH'*2;
#3~hF)u&/ % Reference:
6[x6:{^J % by 平先军.一种新的分数阶傅立叶变换快速算法.电子学报.
gI T3A*x % 2001(3),Vol.29:406-408.