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。
nJldz; DGa#d_I function FF=frft_PXJ(N,alpha);
Jo7fxWO_g %matrix
abTDa6 /`v % FF is the kernel matrix of fractional Fourier transform
c]s(u+i % \copyright: zjliu
<t?x 'r?@ % Author's email:
zjliu2001@163.com +X* F<6mZ Ts=sqrt(2*pi/N); t=-(N-1)/2:(N-1)/2; t=t'; t=t*Ts;
xVsa,EX b variance=N/2/pi; HH=zeros(N); HH(:,1)=1; HH(:,2)=2*t;
(!3Yc:~RE for k=3:N;
27Kc-rcB HH(:,k)=HH(:,k-1).*t*2-2*(k-2)*HH(:,k-2);
;1{iF2jZ: end
~h>rskJ_ HH(:,1)=1/sqrt(sqrt(variance))*HH(:,1).*exp(-t.*t/2);
EFa{O`_@U for k=2:N;
2cs?("8e% HH(:,k)=exp(-t.*t/2).*HH(:,k)/sqrt(2.^(k-1)*...
x"(7t3xK factorial(k-1)*sqrt(variance));
b[J-ja.
end
LCo1{wi if mod(N,2)==1;
i63`B+L{ W=0:N-1; k=exp(-i*alpha*W); D=diag(k);
ESC else
6pM"h5hA W=0:N-2; W=cat(2,W,[N]); k=exp(-i*alpha*W); D=diag(k);
F9m 2C'U end
[<en1 FF=Ts*HH*D*HH'*2;
_9Dn\=g % Reference:
Ek"YM[ % by 平先军.一种新的分数阶傅立叶变换快速算法.电子学报.
O_r^oH % 2001(3),Vol.29:406-408.