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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.h pwS"BTZ function FF=frft_PXJ(N,alpha);
guGX
G+ %matrix
' (XB|5 % FF is the kernel matrix of fractional Fourier transform
#"?pY5 (" % \copyright: zjliu
e8wPEDN*4 % Author's email:
zjliu2001@163.com _x3=i\O, Ts=sqrt(2*pi/N); t=-(N-1)/2:(N-1)/2; t=t'; t=t*Ts;
;H`@x Lv* variance=N/2/pi; HH=zeros(N); HH(:,1)=1; HH(:,2)=2*t;
=<m!%/I for k=3:N;
B:0oT HH(:,k)=HH(:,k-1).*t*2-2*(k-2)*HH(:,k-2);
Oq,@{V@)9k end
K|$c#X HH(:,1)=1/sqrt(sqrt(variance))*HH(:,1).*exp(-t.*t/2);
OI"g-+~ for k=2:N;
G!=(^G@J; HH(:,k)=exp(-t.*t/2).*HH(:,k)/sqrt(2.^(k-1)*...
a~a:mM>p factorial(k-1)*sqrt(variance));
#Ha"rr46p end
={
-kQq if mod(N,2)==1;
r\F2X J^ W=0:N-1; k=exp(-i*alpha*W); D=diag(k);
ov H'_' else
:@"o.8p W=0:N-2; W=cat(2,W,[N]); k=exp(-i*alpha*W); D=diag(k);
~o|sm a5. end
IDD`N{EA FF=Ts*HH*D*HH'*2;
ebNRZJ?C, % Reference:
tc)Md]S % by 平先军.一种新的分数阶傅立叶变换快速算法.电子学报.
o#1Ta7Ro % 2001(3),Vol.29:406-408.