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。
ZfU_4Pl-> <Vim\ function FF=frft_PXJ(N,alpha);
)'JSu=Ej %matrix
hjE9[{K % FF is the kernel matrix of fractional Fourier transform
`Oi@7/oT % \copyright: zjliu
%}/)_RzQ % Author's email:
zjliu2001@163.com L@wnzt Ts=sqrt(2*pi/N); t=-(N-1)/2:(N-1)/2; t=t'; t=t*Ts;
JsV#: variance=N/2/pi; HH=zeros(N); HH(:,1)=1; HH(:,2)=2*t;
7j+.H/2 for k=3:N;
(w*$~p HH(:,k)=HH(:,k-1).*t*2-2*(k-2)*HH(:,k-2);
="`y<J P end
<FP-]R) HH(:,1)=1/sqrt(sqrt(variance))*HH(:,1).*exp(-t.*t/2);
Po5}Vh for k=2:N;
[kCn6\_<V HH(:,k)=exp(-t.*t/2).*HH(:,k)/sqrt(2.^(k-1)*...
x{rt\OT factorial(k-1)*sqrt(variance));
04s N4C end
wgrYZ^] if mod(N,2)==1;
&>-Cz%IV W=0:N-1; k=exp(-i*alpha*W); D=diag(k);
?NL2|8 else
,#crtX W=0:N-2; W=cat(2,W,[N]); k=exp(-i*alpha*W); D=diag(k);
=c|Bu^(Ctw end
HN:{rAIfc FF=Ts*HH*D*HH'*2;
{1o=/& % Reference:
E^g6,Y:i9 % by 平先军.一种新的分数阶傅立叶变换快速算法.电子学报.
<^=k~7m % 2001(3),Vol.29:406-408.