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。
zG@9-s* L (LRv c!`" function FF=frft_PXJ(N,alpha);
lbT<HWzNH %matrix
\D, 0 % FF is the kernel matrix of fractional Fourier transform
\#2,1W@ % \copyright: zjliu
c2?(.UV % Author's email:
zjliu2001@163.com YcRjbF,|6 Ts=sqrt(2*pi/N); t=-(N-1)/2:(N-1)/2; t=t'; t=t*Ts;
-1S+fUkiK/ variance=N/2/pi; HH=zeros(N); HH(:,1)=1; HH(:,2)=2*t;
;-^WUf| for k=3:N;
w6R=r
n HH(:,k)=HH(:,k-1).*t*2-2*(k-2)*HH(:,k-2);
q'+XTal
end
vT%rg r HH(:,1)=1/sqrt(sqrt(variance))*HH(:,1).*exp(-t.*t/2);
~LO MwMHl for k=2:N;
^o:0 Y}v= HH(:,k)=exp(-t.*t/2).*HH(:,k)/sqrt(2.^(k-1)*...
Lkk'y})/ factorial(k-1)*sqrt(variance));
Sqc*u&W end
t}nZrD if mod(N,2)==1;
.b N0! W=0:N-1; k=exp(-i*alpha*W); D=diag(k);
z~o%U&DO} else
A>7'W\R W=0:N-2; W=cat(2,W,[N]); k=exp(-i*alpha*W); D=diag(k);
0[PPVr: end
[ "J FF=Ts*HH*D*HH'*2;
X-oou'4< % Reference:
o0s+ roiD % by 平先军.一种新的分数阶傅立叶变换快速算法.电子学报.
rI;e!EW % 2001(3),Vol.29:406-408.