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。
v`beql
h/-7;Csv function FF=frft_PXJ(N,alpha);
3^1)W!n/ %matrix
>{Lfrc1 % FF is the kernel matrix of fractional Fourier transform
<uv{/L
b % \copyright: zjliu
>SfC '* 1 % Author's email:
zjliu2001@163.com Arfq Ts=sqrt(2*pi/N); t=-(N-1)/2:(N-1)/2; t=t'; t=t*Ts;
R&PQ[ Xc variance=N/2/pi; HH=zeros(N); HH(:,1)=1; HH(:,2)=2*t;
0SvPyf%AC for k=3:N;
v6f$N+4c HH(:,k)=HH(:,k-1).*t*2-2*(k-2)*HH(:,k-2);
Wc`Vcn1 end
Vy-S9= HH(:,1)=1/sqrt(sqrt(variance))*HH(:,1).*exp(-t.*t/2);
Nmi#$K[x for k=2:N;
7^|3TTK HH(:,k)=exp(-t.*t/2).*HH(:,k)/sqrt(2.^(k-1)*...
b;!ilBc factorial(k-1)*sqrt(variance));
U@Aq@d+n end
B#EF/\5 if mod(N,2)==1;
36Wuc@<H W=0:N-1; k=exp(-i*alpha*W); D=diag(k);
PO)5L else
Av+
w>~/3 W=0:N-2; W=cat(2,W,[N]); k=exp(-i*alpha*W); D=diag(k);
B*DH^";t end
L=HL1Qe$G] FF=Ts*HH*D*HH'*2;
xW"J@OiKL % Reference:
/_jApZz % by 平先军.一种新的分数阶傅立叶变换快速算法.电子学报.
+H="5uO< % 2001(3),Vol.29:406-408.