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。
q|S }5 GSk;~^l function FF=frft_PXJ(N,alpha);
$ED<:[3N %matrix
K\uR=L7 % FF is the kernel matrix of fractional Fourier transform
,ujoGSx} % \copyright: zjliu
4YKb~1qkk % Author's email:
zjliu2001@163.com *b> ~L Ts=sqrt(2*pi/N); t=-(N-1)/2:(N-1)/2; t=t'; t=t*Ts;
lO:[^l?F variance=N/2/pi; HH=zeros(N); HH(:,1)=1; HH(:,2)=2*t;
<@oK^ja for k=3:N;
xC|7"N^/ HH(:,k)=HH(:,k-1).*t*2-2*(k-2)*HH(:,k-2);
<h(tW end
s{gdTG6v` HH(:,1)=1/sqrt(sqrt(variance))*HH(:,1).*exp(-t.*t/2);
Up8#Nz
T for k=2:N;
+YP,LDJ!v HH(:,k)=exp(-t.*t/2).*HH(:,k)/sqrt(2.^(k-1)*...
}v`5
factorial(k-1)*sqrt(variance));
MgA6/k end
7dAa~!/( if mod(N,2)==1;
ZMbv1*Vt W=0:N-1; k=exp(-i*alpha*W); D=diag(k);
(}'0K? else
y6$5meh.T W=0:N-2; W=cat(2,W,[N]); k=exp(-i*alpha*W); D=diag(k);
`/"TYR% end
z55P~p FF=Ts*HH*D*HH'*2;
@dGj4h. % Reference:
p!173y,nL % by 平先军.一种新的分数阶傅立叶变换快速算法.电子学报.
hMdsR,Iq % 2001(3),Vol.29:406-408.