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。
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gE1" .qC function FF=frft_PXJ(N,alpha);
Zh@\+1] %matrix
b~}}{fm&f % FF is the kernel matrix of fractional Fourier transform
CJ_B. % \copyright: zjliu
N@}U ;x} % Author's email:
zjliu2001@163.com >qCT#TY Ts=sqrt(2*pi/N); t=-(N-1)/2:(N-1)/2; t=t'; t=t*Ts;
y4') !e variance=N/2/pi; HH=zeros(N); HH(:,1)=1; HH(:,2)=2*t;
@OpcS>:R for k=3:N;
dU,/!|.K HH(:,k)=HH(:,k-1).*t*2-2*(k-2)*HH(:,k-2);
LPC7Bdjz end
lk80)sTZ HH(:,1)=1/sqrt(sqrt(variance))*HH(:,1).*exp(-t.*t/2);
dZ*o H#B for k=2:N;
!s$fqn
6 HH(:,k)=exp(-t.*t/2).*HH(:,k)/sqrt(2.^(k-1)*...
[LCi, factorial(k-1)*sqrt(variance));
y$WS;# end
&m` if mod(N,2)==1;
VaB7)r W=0:N-1; k=exp(-i*alpha*W); D=diag(k);
{R K#W~h else
wP%;9y2B W=0:N-2; W=cat(2,W,[N]); k=exp(-i*alpha*W); D=diag(k);
z,)Fvs4U. end
<YC{q>EMc FF=Ts*HH*D*HH'*2;
f: Rh9 % Reference:
cMj<k8.{ % by 平先军.一种新的分数阶傅立叶变换快速算法.电子学报.
~'ovJ46tx % 2001(3),Vol.29:406-408.