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。
@3 + ^^24a_+2 function FF=frft_PXJ(N,alpha);
LaZ
@4/z! %matrix
|Q@( <'8= % FF is the kernel matrix of fractional Fourier transform
Im};wJ& % \copyright: zjliu
G(o6/ % Author's email:
zjliu2001@163.com DY/%|w*L Ts=sqrt(2*pi/N); t=-(N-1)/2:(N-1)/2; t=t'; t=t*Ts;
0"N4WH O variance=N/2/pi; HH=zeros(N); HH(:,1)=1; HH(:,2)=2*t;
cG 3tn&AXi for k=3:N;
h/y0Q~|/d HH(:,k)=HH(:,k-1).*t*2-2*(k-2)*HH(:,k-2);
M0e&GR8<z> end
%s5(''a. HH(:,1)=1/sqrt(sqrt(variance))*HH(:,1).*exp(-t.*t/2);
(KfQ'B+ for k=2:N;
x%T^:R HH(:,k)=exp(-t.*t/2).*HH(:,k)/sqrt(2.^(k-1)*...
0R0_UvsXU factorial(k-1)*sqrt(variance));
D vN0h(? end
Yt_t> if mod(N,2)==1;
.b!HEi<F W=0:N-1; k=exp(-i*alpha*W); D=diag(k);
_5b~3K/V else
7fd,I% v W=0:N-2; W=cat(2,W,[N]); k=exp(-i*alpha*W); D=diag(k);
+# !?+'A end
X4Uy3 TV> FF=Ts*HH*D*HH'*2;
v}z^M_eFm % Reference:
X'%BS % by 平先军.一种新的分数阶傅立叶变换快速算法.电子学报.
U[q3 9FR % 2001(3),Vol.29:406-408.