轉(zhuǎn)載一個實現(xiàn)分數(shù)傅立葉變換的matlab程序，作者信息在程序中有。
Q HmF,P /t=Fx94 function FF=frft_PXJ(N,alpha);
gAxf5 A_x) %matrix
wUJ>?u9 % FF is the kernel matrix of fractional Fourier transform
kl+^0 i % \copyright: zjliu
g\~n5= -D % Author's email:
zjliu2001@163.com q7kE+z Ts=sqrt(2*pi/N); t=-(N-1)/2:(N-1)/2; t=t'; t=t*Ts;
D.:6X'hp variance=N/2/pi; HH=zeros(N); HH(:,1)=1; HH(:,2)=2*t;
?VRf5 Cr- for k=3:N;
NG\g_^.M HH(:,k)=HH(:,k-1).*t*2-2*(k-2)*HH(:,k-2);
c80!Ub@ end
o >Faq+@ HH(:,1)=1/sqrt(sqrt(variance))*HH(:,1).*exp(-t.*t/2);
F!*tE&Se+ for k=2:N;
l1#F1q`^t HH(:,k)=exp(-t.*t/2).*HH(:,k)/sqrt(2.^(k-1)*...
ziXZJ^(FI factorial(k-1)*sqrt(variance));
Bh0hUE end
3 <A$ lG if mod(N,2)==1;
&cuDGo . W=0:N-1; k=exp(-i*alpha*W); D=diag(k);
s1kG:h2 |$ else
HB :VpNFn W=0:N-2; W=cat(2,W,[N]); k=exp(-i*alpha*W); D=diag(k);
{1Hs5bg@ end
5u=$m^@{ FF=Ts*HH*D*HH'*2;
efUa[XO % Reference:
a]4h5kJ'; % by 平先軍.一種新的分數(shù)階傅立葉變換快速算法.電子學(xué)報.
NR9=V % 2001(3),Vol.29:406-408.
