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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&U function FF=frft_PXJ(N,alpha);
n\3#69VY %matrix
,G g;:)k\ % FF is the kernel matrix of fractional Fourier transform
QS5t~rb % \copyright: zjliu
-z0;4O (K] % Author's email:
zjliu2001@163.com N2"B\ Ts=sqrt(2*pi/N); t=-(N-1)/2:(N-1)/2; t=t'; t=t*Ts;
.7
0 variance=N/2/pi; HH=zeros(N); HH(:,1)=1; HH(:,2)=2*t;
;RRw-|/Wm for k=3:N;
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HH(:,k)=HH(:,k-1).*t*2-2*(k-2)*HH(:,k-2);
V~ORb1 end
kDMvTVd HH(:,1)=1/sqrt(sqrt(variance))*HH(:,1).*exp(-t.*t/2);
(+[%^96 for k=2:N;
.
ump?
M HH(:,k)=exp(-t.*t/2).*HH(:,k)/sqrt(2.^(k-1)*...
r9Ogez ER factorial(k-1)*sqrt(variance));
6{Q-]LOc[. end
V`1{*PrI@L if mod(N,2)==1;
j~G(7t W=0:N-1; k=exp(-i*alpha*W); D=diag(k);
dpw-a4o} else
Cj<8r S4+ W=0:N-2; W=cat(2,W,[N]); k=exp(-i*alpha*W); D=diag(k);
{;u,04OVK end
.8u@/f%pV FF=Ts*HH*D*HH'*2;
XFvl % Reference:
BEvY&3%l % by 平先军.一种新的分数阶傅立叶变换快速算法.电子学报.
5dI=;L>D % 2001(3),Vol.29:406-408.