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。
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5'mpd function FF=frft_PXJ(N,alpha);
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Sa %matrix
O*:8gu'Y2 % FF is the kernel matrix of fractional Fourier transform
)dMXn2O % \copyright: zjliu
[Dv6z t> % Author's email:
zjliu2001@163.com VY#:IE:T Ts=sqrt(2*pi/N); t=-(N-1)/2:(N-1)/2; t=t'; t=t*Ts;
S7A[HG; variance=N/2/pi; HH=zeros(N); HH(:,1)=1; HH(:,2)=2*t;
OSDx for k=3:N;
r'GD HH(:,k)=HH(:,k-1).*t*2-2*(k-2)*HH(:,k-2);
5IsRIz[`TK end
IdzrQP HH(:,1)=1/sqrt(sqrt(variance))*HH(:,1).*exp(-t.*t/2);
B\ITXmd
for k=2:N;
*GMs>"C HH(:,k)=exp(-t.*t/2).*HH(:,k)/sqrt(2.^(k-1)*...
-j<g}IG factorial(k-1)*sqrt(variance));
yE80*C~d end
&E{i#r)'T if mod(N,2)==1;
$d +n},[C{ W=0:N-1; k=exp(-i*alpha*W); D=diag(k);
:/1/i&a else
xwm-)~L4T W=0:N-2; W=cat(2,W,[N]); k=exp(-i*alpha*W); D=diag(k);
WL6p+sN' end
\B$Q%\- PX FF=Ts*HH*D*HH'*2;
?#cX_ % Reference:
uINm>$G,5 % by 平先军.一种新的分数阶傅立叶变换快速算法.电子学报.
82q_"y>6 % 2001(3),Vol.29:406-408.