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。
XKq@]=\F Dw |3Z function FF=frft_PXJ(N,alpha);
CW:gEm+ %matrix
pIVq("& % FF is the kernel matrix of fractional Fourier transform
?En7_X{C? % \copyright: zjliu
" OGdE_E % Author's email:
zjliu2001@163.com vS M_]fn Ts=sqrt(2*pi/N); t=-(N-1)/2:(N-1)/2; t=t'; t=t*Ts;
"E>t,
D variance=N/2/pi; HH=zeros(N); HH(:,1)=1; HH(:,2)=2*t;
WL\^F#: for k=3:N;
y3yvZD HH(:,k)=HH(:,k-1).*t*2-2*(k-2)*HH(:,k-2);
lEfBe)7+ end
DuF7HTN[K HH(:,1)=1/sqrt(sqrt(variance))*HH(:,1).*exp(-t.*t/2);
7Qh_8M for k=2:N;
@8"18HEp# HH(:,k)=exp(-t.*t/2).*HH(:,k)/sqrt(2.^(k-1)*...
Yg6If7& factorial(k-1)*sqrt(variance));
>QI~`MiI end
m1e b8yX if mod(N,2)==1;
f[qPG& W=0:N-1; k=exp(-i*alpha*W); D=diag(k);
Z5>V{o else
n(jjvLf W=0:N-2; W=cat(2,W,[N]); k=exp(-i*alpha*W); D=diag(k);
nC~fvyd<P end
8^w/HCC8O FF=Ts*HH*D*HH'*2;
y`b\;kd % Reference:
>38
Lt\ % by 平先军.一种新的分数阶傅立叶变换快速算法.电子学报.
6wpU6NU % 2001(3),Vol.29:406-408.