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。
vLBuE 4_sJ0 =z- function FF=frft_PXJ(N,alpha);
7l[@c|e %matrix
{2mF\A#. % FF is the kernel matrix of fractional Fourier transform
m#i4_F=^b % \copyright: zjliu
!]Qk?T~9- % Author's email:
zjliu2001@163.com VBS}2>p Ts=sqrt(2*pi/N); t=-(N-1)/2:(N-1)/2; t=t'; t=t*Ts;
60cQ3.e variance=N/2/pi; HH=zeros(N); HH(:,1)=1; HH(:,2)=2*t;
Gqc6]{ for k=3:N;
*9xxX,QT8Q HH(:,k)=HH(:,k-1).*t*2-2*(k-2)*HH(:,k-2);
jT< I`K* end
Di27=_J HH(:,1)=1/sqrt(sqrt(variance))*HH(:,1).*exp(-t.*t/2);
Q672iR\#) for k=2:N;
43-Bx`6\ HH(:,k)=exp(-t.*t/2).*HH(:,k)/sqrt(2.^(k-1)*...
g5"I{ol5T~ factorial(k-1)*sqrt(variance));
I8% -ii end
9_F&G('V{a if mod(N,2)==1;
BDzAmrO< W=0:N-1; k=exp(-i*alpha*W); D=diag(k);
J/E''* else
3$q#^UvD W=0:N-2; W=cat(2,W,[N]); k=exp(-i*alpha*W); D=diag(k);
w{|`F>f9 end
8y FF=Ts*HH*D*HH'*2;
D&I/Tbc % Reference:
!Ur.b
@ke % by 平先军.一种新的分数阶傅立叶变换快速算法.电子学报.
:T?WN+3 % 2001(3),Vol.29:406-408.