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。
8Rd*`]@[pk eGlPi| function FF=frft_PXJ(N,alpha);
S,^)\=v %matrix
nB#XQ8Nzx^ % FF is the kernel matrix of fractional Fourier transform
bLyaJ%pa\/ % \copyright: zjliu
c>yqq' % Author's email:
zjliu2001@163.com nQ^ c{Bm: Ts=sqrt(2*pi/N); t=-(N-1)/2:(N-1)/2; t=t'; t=t*Ts;
629#t`W\ variance=N/2/pi; HH=zeros(N); HH(:,1)=1; HH(:,2)=2*t;
(b;*8 for k=3:N;
"tg?V HH(:,k)=HH(:,k-1).*t*2-2*(k-2)*HH(:,k-2);
*waaM]u end
T8-,t];i HH(:,1)=1/sqrt(sqrt(variance))*HH(:,1).*exp(-t.*t/2);
P^& =L&U for k=2:N;
n_MY69W HH(:,k)=exp(-t.*t/2).*HH(:,k)/sqrt(2.^(k-1)*...
6@geakq factorial(k-1)*sqrt(variance));
0m&W: c end
05/'qf7P,U if mod(N,2)==1;
cP`[/5R W=0:N-1; k=exp(-i*alpha*W); D=diag(k);
\LQ54^eB else
v0'`K 5M W=0:N-2; W=cat(2,W,[N]); k=exp(-i*alpha*W); D=diag(k);
f|'8~C5I@> end
;n;bap FF=Ts*HH*D*HH'*2;
Kz2s{y~? % Reference:
#^eXnhj 9 % by 平先军.一种新的分数阶傅立叶变换快速算法.电子学报.
}J|Pd3Q Sf % 2001(3),Vol.29:406-408.