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。
gN,O)@N'd3 @uh^)6i]/ function FF=frft_PXJ(N,alpha);
dTV4 Q`Z %matrix
`ChS$p"A % FF is the kernel matrix of fractional Fourier transform
`IP?w&k) % \copyright: zjliu
0 ge"ISK % Author's email:
zjliu2001@163.com "_LDs(& Ts=sqrt(2*pi/N); t=-(N-1)/2:(N-1)/2; t=t'; t=t*Ts;
CbvP1*1 variance=N/2/pi; HH=zeros(N); HH(:,1)=1; HH(:,2)=2*t;
968<yO] for k=3:N;
s9[?{}gd HH(:,k)=HH(:,k-1).*t*2-2*(k-2)*HH(:,k-2);
:n#8/'%1 end
g mdJ8$ HH(:,1)=1/sqrt(sqrt(variance))*HH(:,1).*exp(-t.*t/2);
FEC`dSTI for k=2:N;
/KU9sIE; HH(:,k)=exp(-t.*t/2).*HH(:,k)/sqrt(2.^(k-1)*...
?*oBevUnCY factorial(k-1)*sqrt(variance));
U yb -feG end
]=gNA if mod(N,2)==1;
kM:Z(Z7$ W=0:N-1; k=exp(-i*alpha*W); D=diag(k);
x;^DlyyYU else
-yP|CZM W=0:N-2; W=cat(2,W,[N]); k=exp(-i*alpha*W); D=diag(k);
-_*ux! end
2XX- FF=Ts*HH*D*HH'*2;
v3p0 % Reference:
#mIgk'kW< % by 平先军.一种新的分数阶傅立叶变换快速算法.电子学报.
M]Kxg; % 2001(3),Vol.29:406-408.