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。
:b,An'H "!:)qVL^ function FF=frft_PXJ(N,alpha);
X#ud_+6x %matrix
D@m3bsMwe % FF is the kernel matrix of fractional Fourier transform
b{.Y?.U % \copyright: zjliu
jPs{Mr< % Author's email:
zjliu2001@163.com S) `@)sr Ts=sqrt(2*pi/N); t=-(N-1)/2:(N-1)/2; t=t'; t=t*Ts;
|W5lhx0U variance=N/2/pi; HH=zeros(N); HH(:,1)=1; HH(:,2)=2*t;
9T<k|b[6 for k=3:N;
FaKZ|~Y
e HH(:,k)=HH(:,k-1).*t*2-2*(k-2)*HH(:,k-2);
hcR^? end
*`t3z-L HH(:,1)=1/sqrt(sqrt(variance))*HH(:,1).*exp(-t.*t/2);
-gv[u,R for k=2:N;
.i1|U8" X HH(:,k)=exp(-t.*t/2).*HH(:,k)/sqrt(2.^(k-1)*...
5YXMnYt9 factorial(k-1)*sqrt(variance));
+^[SXI^JaJ end
Q'aVdJN, if mod(N,2)==1;
BuOe'$F
0t W=0:N-1; k=exp(-i*alpha*W); D=diag(k);
=h/61Bl3 else
27Vx<W W=0:N-2; W=cat(2,W,[N]); k=exp(-i*alpha*W); D=diag(k);
Q 34-a"6) end
m"
]VQnQ FF=Ts*HH*D*HH'*2;
,8stEp9~h] % Reference:
S~^]ib0 % by 平先军.一种新的分数阶傅立叶变换快速算法.电子学报.
SfPtG % 2001(3),Vol.29:406-408.